Mono on Mac: DllNotFoundException despite SQLite.Interop.dll being in diretory and in $PATH

I have a C# application that uses SQLite and works fine on Windows.

The same Visual Studio project compiles fine in Xamarin Studio, but when running I get:

DllNotFoundException: SQLite.Interop.dll

Despite:

• SQLite.Interop.dll being in the same folder as the executable and other DLLs
• . being part of the $PATH
• My code does not contain any DllImport

What is the problem?