Does anyone have any idea on how to approach contact resistance calculation and measurement between 2 conductive foils of different materials (and different areas), say Cu + Alu? Thanks in advance.

I would suggest you approach the problem by passing a known current through the connection and measuring the resulting voltage drop across the contacts. Then calculate the contact resistance R = V/I. that is the traditional method used by high-current test sets for measuring the contact resistance of circuit breakers. Since the contact resistance is very small, you will need a large current and a very sensitive volt meter capable of measuring in the milli-volt and micro-volt ranges.

there's a milli ohmmeter in the market that you can check for the contact resistance in circuit breakers...

It doesn't really matter what is the type of materials. Any electrical contact point should be as near to zero resistance as possible. Micro ohms are desired. NETA (interNational Electrical Testing Association) has excellent references for testing standards.

Jim has already given the correct answer about one method of measuring contact resistance.
It is well known that the contact resistance is a function of the material resistivity and surface of material exposed to contact. Instead, a simple measurement with an ordinary instrument can be negatively influenced by the generated contact potential between the two materials, e.g. between Cu and Al in which one is electropositive and the other electronegative.
Successive electroplating procedures in order to cover the surface of the materials in contact using metals having progressive native potential, counteract these phenomena.

we also do silver electroplating in our hydrogen plant busbar joints... this inhibits temp rise in the busbars and also makes the assy pass the contact resistance test...