Is there a simple circuit that outputs (min+max)/2 of a single-ended signal given as input?
As has been implied in comments, if there is a digital 1 or zero event for some lengthy period of time any peak measurement made will need to rely on analogue values being held on a capacitor and no, there is no way of passively achieving this. 

I have previously done this by using "peaks detectors" (an opamp with diode and capacitor) for "storing" the most positive voltage and the most negative voltage - two peak detector circuits are needed. Also, some modest amount of low-pass filtering is needed to be done on the raw signal to prevent noise spikes causing too much of an accuracy limit. Here is the general idea for detecting the most positive peak of the signal: -



For my application the detector needed to be done at very high speeds because I was trying to implement a special circuit for detecting and resolving corrupted high speed data. I used a MAX999 comparator for each peak detection circuit.

If your data rate is modest, a better way would be to use a microprocessor and an ADC and actually measure the levels.

Producing a third voltage (or number) that is the mean of the two levels is of course trivial in comparison.