I've had a coupla beers tonight so not sure how clear this will sound ...
I believe you can mix them, but you'd have to experiment to make it work. Active pickups have a preamp on board. They'll have a higher signal and less impedance than will their passive counterparts. When you attempt to combine the two at the output, the higher signal and lowered impedance from the active pickups will likely dominate the signal.
So, I think you could make this work, but you'd either need to wire the passive pickup through the preamp in some way or reduce the output of the active pickups (via resistance, etc.) to even out the signal.
Would actually be fun to experiment with, but lots more hassle than just picking up a beefier EMG for the bridge. Or, if you opt to replace everything with passive pickups, there are quite a few good brands of noise-free single coils you can use. (I prefer Bill Lawrence 280s but there are lots of others.)