Question: Are there any tools for memory profiling of applications that consist of `C#` and `Delphi` parts?

These two parts cannot be started separately - its one Application. `C#` and `Delphi` communicate via `COM` with each others.

*Update*
I have tried `dotTrace Memory 3.5` - application crashed with Exception in `clr.dll.` I can start the application via profiler - choice *Mark Memory* - the crash occur if I want to get a snapshot.

Answer: 
I assume you compile them separately, which means that they can be profiled separately. Depending on your version of delphi, AQTime comes with it for gross profiling from the debugger.

I can't really help with the C# portion, but I assume profilers exist, perhaps in Microsofts own tool chain, that can also be run from the IDE.
dotTrace Memory or Scitech memory profiler for .NET and AQTime or FastMM for Delphi, just use them together. I don't know any integrated solution.