Both egg white and cream can be beaten until they form a stiff foam. So I tried mixing them and beating the mixture. The mixture will not rise (foam) no matter how hard I try. What is the reason behind this?
I assume by 'rise' you mean 'can be beaten into a foam' (rather than increasing in volume like leavening bread or a cake in an oven).
Egg white and whipped cream both trap air bubbles when whipped, but the bubbles are supported by different structures. Egg white forms a network of protein, which even small amounts of fat will disrupt (as is often the problem when eggs are not properly separated before whipping). Whipped cream relies on fat for the structure that holds the air bubbles (so cream below a certain fat content will not whip).
When combined, these mechanisms disrupt each other so you should not expect to be able to whip a mixture of egg white and cream. Instead, you can whip them separately and fold the results together until they are just combined (if you mix them too much the foam will be ruined).