The House passed the final defense authorization last night, as President Barack Obama’s administration relented on its veto threat despite continued questions about military-detainee language.

House and Senate negotiators filed the compromise bill Monday night, saying they believed tweaks they made to military-detainee provisions in it would quash a veto threat from the White House.

The House passed the bill via a 283-136 vote last night, sending it to the Senate for final vote, after the Obama administration relented on its veto threat. Still, FBI Director Robert Mueller told the Senate Judiciary Committee yesterday the changes “did not really fully address” his “concerns” about clarifying the authorities of civilian and military officials dealing with terrorism suspects.

House Armed Service Committee (HASC) members from both parties defended the bill on the House floor yesterday. HASC Ranking Member Adam Smith (D-Wash.), a prosecutor, circulated a “dear colleague” letter defending the detainee provisions in the bill.

The defense authorization bill is for fiscal year 2012, which started Oct. 1. Congress is also in the final stages of passing budget-setting Pentagon appropriations legislation for FY ’12, as part of a larger budget package, though it remained stalled yesterday amid partisan fighting over non-defense matters. The Pentagon and much of the government is running under a temporary budget that expires Friday at midnight.

The defense authorization legislation includes changes to the Pentagon’s plans for weapon systems including Lockheed Martin’s [LMT] F-35 Joint Strike Fighter program. The measure trims the Pentagon’s request for 32 F-35s to 31 and says contracts for forthcoming lots of aircraft must be fixed-price and require the contractor pay all cost overruns.

The authorization bill calls for a $530 billion base defense budget, $23 billion less than the administration’s initial combined $553 billion request for the Pentagon and military construction, which it submitted to Congress in February. The authorization measure also cuts the White House’s war-funding request from $117.8 billion to $16.9 billion.

The appropriations legislation, meanwhile, includes a $518 billion base defense budget, not including military-construction funding, or $21 billion less than the $539 billion in comparable funding the administration proposed in February.

After Obama signed the deficit-cutting Budget Control Act in August, the White House said it supported a $513 billion defense budget, without factoring in military construction.