Is the Motorola an RDM2070d or RM series MURS radio? If so, are you using a standard 3.5mm headset designed for a cell phone? Are you attempting to use the same headset on the Baofeng? If so, you may have a connector mismatch.
The Motorola MURS radios use a two pin Motorola (M1) connector. The UV-5R uses a 2 pin Kenwood (K1) connector. While the two connectors are similar, the pins of the K1 are farther apart and slightly different in length.
Most versions of the UV-5R use the same connector jack as the original. It was specifically designed for use with the K1 connector, so if you are using a a standard consumer grade 3.5mm stereo headset, it isn’t quite compatible with your radio, which is probably why your audio cuts in and out.