I graduated last year and my advisor passed away unexpectedly soon after. What should I do now for subsequent academic job searches?
This is a very difficult situation. As per the comment by Andy Putman, let your other letter writers explain the situation. Considering you got the Postdoc job, your current supervisor must have been impressed with what your advisor said in his letter. Your current supervisor can include a personal story about something your advisor said about you or even include a few of his favorite verbatim quotes about you from the letter of recommendation for your current postdoc. Anyone on a hiring committee will understand, and will possibly even be personally touched. This will not count against you. 

I wouldn't send a copy of your postdoc letter in your application materials If your postdoc supervisor highlighted the strongest quotes from the advisor's letter. If he chooses not to do this or if your advisor's letter in its entirety is much stronger than the best few quotes from it and your postdoc supervisor still has the letter he could send it along with his letter.(note that in other fields this letter may be a bit inappropriate because it could contain a lot of detailed information about how you are a great fit for the particular postdoc position but as Pete points out this usually is not true in pure math).

Unfortunately this does not heal any wounds caused by the unfortunate passing away of your advisor and life long friend, but you should not worry about the letter writing situation. I can't say that I even begin to imagine the emotional pain of losing an advisor so close to graduation, but as someone who lost a parent while in college I greatly sympathize with you and I can think of no greater honor to your advisor than to continue in academia and continue doing great work.