I don't know anything about BlueIris, or the Foscam cameras, but this may be possible using the SDK.
If you can get the software to run a command on the PC with AHP on it, then it should be pretty easy, in fact.
You'll need to download and install the SDK (if you haven't done so already), and then create a macro with a HouseCode/UnitCode trigger (as opposed to a security module trigger).
Then, just have BlueIris trigger the macro using the AHCMD program from the SDK.