But experts and officials say a nuanced look at relations with the two neighbors tells a story of a cold peace that is only growing chillier.
Israeli diplomats with knowledge of both countries were unwilling or unable to openly discuss ties, a resonant reminder that any misplaced statement could destroy the extremely fragile relations.
In Jordan, perceived Israeli violations of the status quo of Jerusalem's holy sites, over which Jordan maintains a custodianship, have angered Amman, and the parliament there recently voted to expel Israeli ambassador Daniel Nevo.
Israel receives "continuous and systematic" complaints about Israeli actions on Jerusalem's Temple Mount, a knowledgeable diplomat told The Times of Israel, but added that Israeli-Jordanian relations are "mature" in the understanding of both sides of how important the relations are.
Still, Israel's relations with Jordan are now at a low point, the diplomat said, though not the lowest they've ever been. He was likely referring to the crisis that followed Israel's botched assassination attempt of Hamas political leader Khaled Mashaal in Amman in September 1997.
Added to the mix is the elephant in the room the Israeli-Palestinian conflict which heavily colors relations with both Cairo and Amman.
"Israel and Jordan are on a strategic collision course," said Assaf David, who teaches Jordanian politics at Jerusalem's Hebrew University. "If no two-state solution emerges, at whose expense will the Palestinian issue be resolved?"
In Amman, security considerations prevent Israeli diplomats from living with their families. The embassy staff cross the Allenby Bridge over the Jordan River every weekend to spend time with their loved ones. On January 14, 2010, two roadside charges were detonated next to a diplomatic convoy traveling from the embassy to Allenby Bridge. The ambassador, who was in one of the vehicles, was not harmed, but the two vehicles were.
David says that Israel and Jordan's diplomatic ties and security cooperation are vastly disconnected, the former gradually declining since the Mashaal assassination attempt in 1997 and the latter remaining consistently good. But as long as no hope exists for a peaceful resolution of the Palestinian issue, Israel and Jordan can never normalize relations.
Nevertheless, with few Arab allies in the region, King Abdullah is, "unbearably, as far as he's concerned," dependent on Benjamin Netanyahu as a strategic partner to counter the Syrian threat, David said.
Shimon Shamir, an emeritus professor at Tel Aviv University who served both as Israel's first ambassador to Jordan (starting in 1994), and as ambassador to Egypt (from 1988 to 1990), claimed that neither Israel nor Jordan invested adequate efforts in maintaining their strategic alliance.
In a book published last year titled "The Rise and Fall of the Warm Peace with Israel," Shamir argues that, unlike the Camp David Peace accords with Egypt which were largely a strategic agreement designed to prevent another war the agreement with Jordan was about cooperation and normalization.
"Half of the peace agreement with Jordan deals with cooperation. That's the crux of the agreement. It was supposed to be an opening to a different kind of peace, not like the one with Egypt."
Israel unnecessarily embarrassed King Hussein a staunch supporter of warm peace with Israel by attempting to assassinate Hamas leader Mashaal, he claimed.
"Israel should have understood that we are in the same boat as Jordan," said Shamir.
A number of ambitious joint projects with Jordan "which were meant to change the face of the Middle East" never materialized, Shamir added, due to a lack of political will on both sides a joint airport, a joint seaport, an industrial park near the Dead Sea, and a canal connecting the Red and Dead seas.
The situation in Egypt is even gloomier.
Israeli officials tacitly indicate that Israel has grudgingly agreed to forgo the pleasures of normalization with Egypt in order to maintain the tight security coordination with its military establishment, especially at a time when terrorism in Sinai is rampant. Keeping jihadists at bay continues to be a strong, joint interest of both Egypt and Israel.
Israel can never normalize its relations with Egypt as long as the conflict with the Palestinians remains unresolved, Shamir said. But he still believed that things could be worse.
"One encouraging thing is that there is almost no opposition to the very idea of peace with Israel," he said.
The popular demonstrations that toppled Hosni Mubarak in February 2011 quickly engulfed the Israeli Embassy in Cairo, which was closely associated with the former regime in public perception.
In September 2011, angry protesters broke through the embassy walls and stormed the building, removing the Israeli flag and coming within one room of the Israeli staff and security detail. An Egyptian elite force prevented a massacre at the last moment, but the embassy was ransacked and subsequently shut by authorities.
In the 21 months since, an alternative embassy was never found; the official reason is the inability to locate a building with adequate security provisions. As of today, the embassy staff hold meetings in public locations around Cairo, shuttling back and forth to and from Israel.
"That situation is certainly abnormal," Shamir claimed, noting that from his first day in office he realized that the embassy, situated near the riotous campus of Cairo University, was badly located.
Yitzhak Levanon, who served as Israel's ambassador to Cairo when the mob stormed his embassy, told The Times of Israel last September that the gradual deterioration in relations began as early as Hosni Mubarak's rise to power in 1981, but has accelerated since the election of President Mohammed Morsi last June.
"The Muslim Brotherhood is simply not interested in normalization," Levanon said. "Israel will need to get used to that new reality."
But though Shamir says the peace with Egypt was born of convenience and not true friendship, he says his time as ambassador in the late 1980s was marked by a high level of cooperation.
"In my time, the relations with Egypt were much closer," he recalled. "We had joint projects: First we bought oil and then we started to buy natural gas, before that too stopped. El Al flights took place a few times a week, with delegations visiting almost every week. All this no longer exists."