Heat capacity of mixtures
Suppose you have $n_1$ mole of A and $n_2$ mole of B. If they are at temp. $T_1$ and you want to raise the temp. to $T_2$ then the amount of heat you need to add is
$$\Delta H~= n_1 \times c_{pA} \times \Delta T + n_2 \times c_{pB} \times \Delta T$$
$$\Delta H~= (n_1 \times c_{pA} + n_2 \times c_{pB}) \times \Delta T$$
$$\Delta H~= (n_1 +n_2)\times \frac{(n_1 \times c_{pA} + n_2 \times c_{pB})}{(n_1+n_2)} \times \Delta T$$
$$\Delta H~= n_{total} \times(y_1 \times c_{pA} + y_2 \times c_{pB}) \times \Delta T$$
$$\Delta H~= n_{total} \times c_{p,avg} \times \Delta T$$
So basically you are not losing any information in case of ideal situation where molecular interaction of two different species has no effect on each other's heat capacity. But from statistical mechanics we know,
$$C_v=\frac { &lt;E^2&gt;-&lt;E&gt;^2}{k_B \times T^2}$$
Now if we solve the schrodinger equation for individual species, we must include an extra potential energy term to account the interaction from other species, which in turn will result in fluctuation of $C_v$ from it's previous value. 

Slightly off topic: When I see the question first things that came to my mind is kopp's rule. It's used to find heat capacity of molecule using atom's heat capacity or to find alloy's heat capacity using the constituents heat capacity.