Please see my comment to the question. This is a really bad idea. Processes are isolated; they do not collaborate unless they are designed for this purpose (sockets, TCP communication, .NET remoting/WCF…). Due to Windows specifics, you can always stick one window inside another, using (P/Invoked) Windows API working with HWNDs (window handles), so what? What would you do next?
Instead, you could better use something in a single process, on a component level, something like this:
C# MP3 Sound Capturing/Recording Component
Also play attention on the article referenced in the article I referenced above, on the player for the recorded sound:
A low-level audio player in C#