Charge sensitive amplifier operation doubt: Same BNC for two purposes. How?
That's simply a matter of adding a high-pass filter in line: your DC supply won't pass, but high-frequency pulses are let through. In the power line, add a low-pass filter, so that noise generated on the supply rail doesn't bleed back into your signal line:

--PWR+Signal---+----|HPF|---&lt;signal----
               |
               \----|LPF|--&gt;DC----&gt;


This is a pretty commonly employed technique in things like RF amplifiers: technically, their core is biased transistors, and you can imprint the biasing from the supply, using pretty much the inverse to the above (called a bias-T, often for the fact that it's a T-junction that adds a bias):

--PWR+Signal---+----|HPF|---&lt;signal----
               |
               \----|LPF|---&lt;DC----&lt;power supply