We're getting ready to go to Israel/Jordan next May, and would like to do a multi-city trip. We would land at Ben Gurion in Israel and would like to fly out of Queen Alia in Jordan. Do we have to have a return ticket when entering Israel, or would showing them a ticket out of Jordan suffice?
Are you booking separate one-way flights? Instead, I would look at Turkish Air and Royal Jordanian. With Turkish, you'd change planes in Istanbul, then direct flights into Tel Aviv and out of Amman. With Jordanian, outbound you'd change planes in Amman to to Tel Aviv.
Between Israel and Jordan, there are 3 land border crossings (check visa requirements into Jordan - you may need to have your visas issued in advance depending on which crossing you use). If you're flying, no problem.
I don't know what information they have at passport control when you present your passport. AFAIK, unless there's some reason to question you (like having visa stamps from certain countries like Egypt, but not Turkey), I think you'd just get an automatic visa issued when you show your US passport. Since lots of tourists visit both countries and use land border crossings, your ticket out of Jordan should suffice. If you have a visa stamp that may bring up questions, they'll take you aside for a short interview. Be open and honest and you'll be fine.