Neat. Surprisingly, there are 388 solutions, and a lot of them look rather unintuitive.

    ........
    ...Q....
    ........
    ........
    .....Q..
    ........
    ........
    Q..B..Q.

    Q.......
    ........
    ........
    ........
    ..QQB..Q
    ........
    ........
    ........

Python script: https://gist.github.com/dllu/698d5f71b2b9735c5c462ddf4a2f6fc...

Here's how it works:

0. precompute the attack patterns of each possible queen/bishop location as a bitmask, stored as an integer

1. generate candidate solutions, allowing attack rays to pass through other pieces, by brute forcing the positions of the 5 pieces and taking the bitwise OR of their attacks

2. out of the candidate solutions, check which ones are actually valid taking into account occlusion. Actually, you only need to check if the queen's horizontal attack is blocked by the bishop, as queens cannot block each other (the blocking queen herself has the same attacks so they effectively pass through each other).