How to install 32 bit library to 32 bit web application running on 64 bit machine?

I'm trying to install a library that calls a separate dll, so I have 2 dll files. Lets call them library.dll and dependency.dll respectively.

If both are 32 bit I get the following error:

Unable to load DLL 'dependency.dll': The specified module could not be found.

If they are both 64 bit, I get the following:

An attempt was made to load a program with an incorrect format. (Exception from HRESULT: 0x8007000B)

I'm guessing library.dll needs to be 32 bit, because the application is 32 bit, but dependency.dll needs to be 64 bit because the machine is 64 bit. Not sure if that's how it works, but I can't get this library to work. Any suggestions?