The policy is clear that they will check through/interline a bag if the layover/connection is 12 hours or less; it isn't clear if they will do this if one is traveling on separate tickets, which the OP stated s/he was traveling on, as the policy states, "...on your ticket," not "...on your tickets."
I booked a business class reward ticket the other day to Australia with the outbound being RDU-SFO-MEL and the inbound just MEL to SFO as Qantas wouldn't allow the routing back to RDU, despite there being inventory on AS from SFO to RDU (this was according to the agent I spoke with after I could not book MEL-SFO-RDU together online). Therefore, I had to buy a second ticket from SFO to RDU (though honestly, I was fine with this because I GOT A BUSINESS CLASS REWARD TICKET ON QANTAS!!!!). Both tickets are on AS stock (while the OP's tix were on AS and JL). I was told that my bag will be checked through to MEL on the outbound despite the long layover of 11h25m at SFO, though it would "would be wise to pack essentials in a carry-on," while on the return I would have to ask at check-in if Qantas would tag my bag all the way through to RDU. The agent told me that they *should* do it since the two are partners, despite it being two separate tickets, and because both tickets were on AS stock, but she made it clear that I would be at the whim of Qantas. I have enough time to clear immigration at SFO, get my bag, and re-check it with Alaska (3 hour layover), but I would of course just prefer it be interlined. But, as was clear from my conversation with the agent, if traveling on two tickets with AS and a partner, the interline agreement is perhaps NOT guaranteed, even if both are on AS stock.