Why do we use composite aluminium or titanium stacks in airplanes?
I've boldfaced the parts of this abstract that answer the question.


  Abstract: Ever since the advent of fiber reinforced polymer materials in the field of Aerospace, Metal-FRP stacks started to gain importance due to their superior fatigue performance, phenomenal low weight and good specific strength. However the machining, specially drilling these multi stack materials has always proved to be a challenge ... The very properties that make the FRP composite superior make it a challenge for machining. The mechanism of machining viewed here is more or less fracturing and breakage of the fibers present in the system. This breakage of fiber also induces fractures in the tool resulting in accelerated tool wear. These characteristics render the process unreliable. Also the temperature during the machining of composites is higher than while machining a metal due to the lower thermal conductive properties of the composite. When two such extremely different elements are brought together in the form of a FRP-Metal stack, various challenges are faced to achieve required hole size, quality, tool life, ...


-- Peter Mueller-Hummel, Prithvi Sripathy, and Abdelatif Atarsia, "Fail Safe Drilling of CFRP/Titanium and /Aluminium Stack with H8 Quality for Aerospace Applications," SAE International, 2013.

Cutting speed, cut depth, and feed rate depend strongly on the particular stack's composition: which metals, which composites (carbon, aramid, fiberglass), their ratio, each layer's thickness.



Metal/composite stacks are used all over an airframe.  The 2011 article "A review: Fibre metal laminates, background, bonding types and applied test methods" by Sinmazçelik et al calls them FML's, fiber metal laminates, and figure 3 from there shows where they're found on the Airbus A380: