This paper deals with the boundedness of integral operators and their commutators in the framework of mixed Morrey spaces. Precisely, we study the mixed boundedness of the commutator [b, I α ], where I α denotes the fractional integral operator of order α and b belongs to a suitable homogeneous Lipschitz class. Some results related to the higher order commutator [b, I α ] k are also shown. Furthermore, we examine some boundedness properties of the Marcinkiewicz-type integral µ Ω and the commutator [b, µ Ω ] when b belongs to the BMO class