Assume that military vehicle A is jamming radio signals from nearby civilian vehicle B.

Would A be able to hear what B is trying to transmit, even while jamming the signal so it can't be received at a distance?

And would A be able to reply so B can hear, without broadcasting it so that distant receivers would pick it up?

Firstly, the jammer is jamming the receiver and not the transmitter, by either being closer to the receiver or more powerful than the transmitter. The receiver locks onto the more powerful signal of the two being simultaneously broadcast on the same frequency, so the other is effectively blocked or "jammed."

Secondly, the operator will usually snip out only critical bits of the message to create the impression that one or the other of them is having a radio malfunction. (The last thing a jammer wants is to be detected.)

I receive on one antenna and transmit (jam) on another antenna (usually directional), so I can hear everything but the bits I snip out when I trip the switch. I have to be able to hear the transmitting station AND the intended recipient to know both WHAT to jam and to get an idea of my effectiveness.

Depending on their range from the jamming signal, other friendlies and enemies could possibly hear all of the transmitted messages, and may or may not be able to detect there is any jamming going on.

The second question about the jamming station being able to talk to the transmitting station is trickier, especially given that the jammer is jamming the station the transmitting station is talking to. It is difficult for the operator to concentrate on the jamming and also play at being an enemy operator.

That's probably more than you needed to know, but there's more to it than that, of course, even just restricting it to the unclassified stuff.

(Edit: Corrected a spelling error.)
(Edit: TMI, edited for (I hope!) more clarity.)

Assuming that A has a strong technology advantage, both hearing what you're jamming and selective transmission to a specific target should be simple enough on the technical side.

The concerns that Warbric mentions about attempting covert jamming are not universally relevant, though they are important in "tactical" jamming. For those reasons and others, "tactical" jamming is always very tricky even with superior technology.

On the other hand, the need to remember that you're jamming the receiver rather than the transmitter is important for all forms of jamming. Usually the simplest way to do this is to put your jammer directly between the transmitter and the receiver (this also makes it fairly easy to pick up a signal that you are jamming, assuming that you have good directional capabilities). It is necessary that you insert some element of your jamming system between the transmitter and receiver if the receiver has a directional antenna, and the same is true of your interception system if the transmitter is directional (note that this is only true if you are both intercepting and jamming, otherwise you can be behind one or the other rather than between them).

Knowing now what you propose, I think most readers would accept it as entirely possible with current technology. Just settle on what kind of commo the good guys are using, abide by any restrictions your choice may introduce, and then forget about it. Focus on what you already do well, and write it.

But I never signed anything about cell=phone networks

In case the link breaks, that is news of the French jamming cell phones in some public places while still permitting emergency service calls to get through, all of which sounds to me like stuff along the lines of what Survivor is suggesting.

(Edit: The link was acting squirrelly, so I added alternate connections at other sources.)

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I wasn't too clear on the intent behind the links I posted, so I apologize for that. I only meant to show a technology that is currently being fairly widely reported and which opens the way somewhat for use of any such similar - but fictional (so far as we know) - methods in a story. The leap for a reader just became a bit easier.

(Edit: Never post while taking a trouble call.)

Mike, you need to jump freq.