Can I load a 32 bit DLL into a 64 bit process on Windows?

No, you can't.

Both 16-bit and 32-bit Windows lived in a 32-bit linear address space. The terms 16 and 32 refer to the size of the offset relative to the selector.

...

First, notice that a full-sized 16-bit pointer and a 32-bit flat pointer are the same size. The value 0x0123:0x467 requires 32 bits, and wow, so too does a 32-bit pointer. This means that data structures containing pointers do not change size between their 16-bit and 32-bit counterparts. A very handy coincidence.

Neither of these two observations holds true for 32-bit to 64-bit thunking. The size of the pointer has changed, which means that converting a 32-bit structure to a 64-bit structure and vice versa changes the size of the structure. And the 64-bit address space is four billion times larger than the 32-bit address space. If there is some memory in the 64-bit address space at offset 0x000006fb`01234567, 32-bit code will be unable to access it. It's not like you can build a temporary address window, because 32-bit flat code doesn't know about these temporary address windows; they abandoned selectors, remember?

http://blogs.msdn.com/oldnewthing/archive/2008/10/20/9006720.aspx

If your .NET application is a website running in IIS you can circumvent it.

An ASP.NET webpage running on IIS on a 64-bit machine will be hosted by a 64-bit version of the w3wp.exe process, and if your webpage uses 32-bit dlls your site will fail.

However in IIS you can go into the Advanced Settings of the Application Pool running the site, and change "Enable 32-bit applications" to true.

So it's still not able to run 32-bit dll inside 64-bit process, but rather it is running w3wp.exe as a 32-bit process instead.