Apioceridae & Mydidae are placed in the ‘orthorrhaphous’ Brachycera within the monophyletic Asiloidea. A number of publications dealt with morphological characters that delimit both taxa.
Check out the Anatomical Atlas of Flies provided by CSIRO Australia for morphological terminology here.
Woodley (1989) was unable to find any autapomorphic features for Apioceridae, but postulated two autapomorphies for the Mydidae:
Yeates & Irwin (1996) found a number of autapomorphies for Apioceridae as well as Mydidae.
There are many more diagnostic morphological characters that are important for identification of species or genera. A detailed review is in preparation.