Okay, I did understand you right. As far as I know, there is no solder that will bond with aluminum and copper. There is aluminum solder, such as "Wonder Rod" and there are plenty of solders for copper, but never the twains shall meet. Bonding the two surfaces together with a thermal epoxy, such as Arctic Silver Epoxy is about as good as you will be able to do. With enough clamping pressure, you should be able to get the interface barrier down to a minimum, but it will still represent a thermally resistive junction between the two metals. Don't get me wrong, that is a common procedure for copper base heatsinks with aluminun fins. As a matter of fact, most dual metal heatsinks do not use any thermal interface material. They just clamp the two together and rivet them, screw them, or rely on the friction of a press fit. The bottom line is, even though it would make for an excellent project, it won't "Set the world on fire" in terms of performance. I, myself, have taken an all aluminum heatsink (FOP-32) and merged it with a 1/4 inch copper plate on the bottom. The copper plate, being almost twice as thermally conductive as aluminum, helps spread the heat across the entire baseplate. The best improvement I ever obtained was on the order of 2C. I'd say the best performance comes from an all copper HSF, followed distantly by a dual metal and then an all aluminum. Forget silver. It's just not that much better than copper to warrant the additional cost and difficulty obtaining machining stock.
Hoot