No, it's either one-way or two-way. One-way is usually prohibited except in a few case, two-way is usually fine unless it violates one of the prohibitions like encryption. Your two-way communications using ham radio are public, not private.

It seems broadcasting is prohibited, but broadcasting is defined as:

> (10) Broadcasting. Transmissions intended for reception by the general public, either direct or relayed.

Edit: quote is take from "Definitions" section of sciurus link.

A two-way conversation that involves short periods of what's technically "broadcasting" is very different from "tune in at 10pm to hear me talk for an hour".