First off "WELDCOME TO THE WORLD'S GREATEST WELDING FORUM!!! :) :) :)"

Well then, if the two dissimilar metals are of a sufficient thickness one can at the very least start off with cold welding;
From "Modern Welding Technology 4th Edition by Howard B. Cary:

Cold Welding (CW) is a solid state welding process in which pressure is used to produce a weld at room temperature with substantial deformation of the weld. Welding is accomplished by using high pressures on clean interfacing materials. Sufficiently high pressures can be obtained with simple hand tools when extremely thin materials are being joined.

When cold welding heavier sections, a press is required to exert sufficient pressure to make a successful weld. Indentations are in the parts being cold welded. The process is readily adaptable to joining ductile metals. Aluminum and Copper are readily cold welded...

Diffusion Welding (DFW) is also a solid state welding process that produces a weld by the application of pressure at elevated temperature with no macroscopic deformation, or relative motion of the workpieces.  A filler metal may be inserted  between the faying surfaces.

The process is used for joining refractory and dissimilar metals at temperatures  that do not affect their metallurgical properties. Heating is usually accomplished by induction, resistance, or a furnace. Atmosphere and vacuum furnaces are used, and for refractory metals a protective inert atmosphere is desirable.

Successful welds have been made on refractory metals at temperatures slightly over half the normal melting temperature of the metal. To accomplish this type of joining, extremely close tolerance joint preparation is required and a vacuum or inert atmosphere is used. The process is used quite extensively for joining dissimilar metals.

There's also a section where thermite welding is used to weld together thick sections of Al to Cu also, and I'll write that in here tomorrow because I'm getting tired now...

The process is considered Diffusion Brazing when a layer of filler metal is placed between the faying surfaces of the parts being joined. These processes are used primarily by the aircraft and aerospace industries. Now, I don't know exactly what you are fabricating together, but here's just an example of diffusion bonding:

http://accelconf.web.cern.ch/accelconf/e04/PAPERS/WEPKF001.PDF

This type of link, I normally do not like to post because of all the advertisements yet nonetheless, this link does cover the majority of Solid State welding processes used to successfully join Aluminum and copper together so it's really a choice on you part as to which one is more suitable for you application:

http://www.welding-technology-machines.info/solid-state-welding-processes/advantages-disadvantages-and-applications-of-diffusion-welding.htm

Here's the homepage:

http://www.welding-technology-machines.info/solid-state-welding-processes/solid-state-welding-processes.htm

http://www.fmet.ugal.ro/Anale/ANALE%202007/ANALE%201-2007/22%20Georgescu.pdf

You can also use a copper-Aluminum transition insert piece, and weld the two base metals to their appropriate  corresponding halves of the transition piece with either SMAW. GTAW, or GMAW. ;) By using this method, you avoid encountering very brittle intermetallic phases within the weld zone which will not be as prevalent in the transition piece fusion zone between the two metals!!! :) :) :)

Well there's a whole bunch more, yet I'm really getting tired and sleepy finally, so I'll stop here for now. ;)

I hope this information and links help... Oh well, I can't sleep yet, so I guess I'll continue... 

This one is an overview on bothe resistance and solid state welding processes from the Edison Welding Institute (EWI):

http://www.ewi.org/capabilities/rssw.asp

This one is from Cambridge University on Diffusion Bonding:

http://www.msm.cam.ac.uk/phase-trans/2005/Amir/bond.html

Here's an application or two where Ultrasonic welding is used to weld Al to Cu:

http://www.amtechultrasonic.com/articles_weldingjournal_0197.asp

Here's a US patent from General Electric on Laser Welding Al to Cu:

http://www.freepatentsonline.com/4224499.pdf

This is an interesting article from the Japanese Welding Research Institute @ Osaka University on Diffusion Welding of Copper to Aluminum:

http://ir.library.osaka-u.ac.jp/metadb/up/LIBJWRIK01/jwri08_01_077.pdf

Here's another company offering ultrasonic welding of Al sheet to Cu sheet:

http://www.staplaultrasonics.com/c2-ultra/ultra.htm

This one is bit far out since it uses a gas gun method to produce an impact weld between an aluminum projectile and a Copper Target:

http://nels.nii.ac.jp/els/110006486026.pdf?id=ART0008511979&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1266137155&cp=

This one is an article covering cold welding of Al to Cu by the use of cogged surfaces from the University of Galati of Romania:

http://www.fmet.ugal.ro/Anale/ANALE%202007/ANALE%201-2007/22%20Georgescu.pdf

Well, that's it for now because I'm sleepy and tired. In conclusion, there are many different welding processes used for dissimilar welding of Al to Cu... It just depends on the specifics of you application on deciding which one is the most advantageous one to use... I hope this helps. ;)

Respectfully,
Henry

How come You never mention that it doesn't work on tin?