Question about combined ac/DC signals
The voltages simply add.  To find the currents, consider any of the possible instantaneous voltages.

For example, let's say you have a 1 V peak audio signal with 3 V DC bias.  That means that the actual voltage can be anywhere from 2 V to 4 V.  To see what your circuit does with that, consider each of the voltages in the range separately.

At the least, consider what happens at the limiting conditions of 2 V and 4 V.  For audio, you want to ensure that the subsequent circuit doesn't clip to either rail, or become non-linear for some other reason.  If the circuit behaves proportionally (to the AC component), then you don't have to analyze all the in-between states.