we have a point P anywhere in the octants(3D space) at which waves are getting superimposed, we have to simply add all the components along x to get the net amplitude at P in x direction, do the same with y and then z to get the result of the superimposition at P in all 3 directions.
Now the trick is that longitudinal waves have disturbances only in forward direction(say z direction). So what !! We can sum up the z direction coordinates to get interference results.
Transverse waves have disturbances in upwards direction(say y). So what!! Simply add the y direction disturbances to have the answer.
So, it doesn't matter whether these waves are longitudinal or transverse. Interference will definitely occur and net amplitude can be calculated too using above theory.