The documentation at msdn.microsoft.com says: "... as if it created the process with the DEBUG_ONLY_THIS_PROCESS flag ...".
This means: When debugging a process with DebugActiveProcess all threads of the process are debugged (of course) but child processes are by not debugged.
To debug child processes too, you may set a breakpoint to the first address of CreateProcess() (to be more precise: CreateProcessA, CreateProcessW, CreateProcessAsUserA, ...). When this breakpoint is entered you modify the flags field so the process is started in suspended state and when the function returns you call DebugActiveProcess.