The CO of his ship can extend his tour of duty to up to 60 months. OBLISERV typically refers to extending one's enlistment in order to get shore duty orders because the EAOS date is too close to the PCS date to get orders. His choices would be to extend his enlistment, or stay on sea duty until he leaves the Navy. This will all depend on his specific timing, rotation date, needs of the Navy, etc. As a SPU in Prototype, I'm not sure why this is even on his radar.
Until your husband has orders, it's subject to change (and even after he can get his orders changed). Keep looking for jobs, just don't close on a house.
You husband's orders will include who he must report to and their contact information.