When comparing each individually generated model's $C_p$ to the number of parameters, which number of parameters is the comparison to? Each individual model or the overall number of parameters?
You compare it to the number of parameters in each individual model. The idea is that for good models, Mallow's $C_p$ is close to the number of parameters, while for poor models it will be much higher. When looking at a large number of models $C_p$ is sometimes plotted against $p$, and then the line $C_p=p$ is drawn in to help with the comparison.
Edit: For an example:
Though they've plotted the line $C_p=p+1$ rather than $C_p=p$.