While my wife was pregnant I decided to start assembling the bits I needed to put together a DIY baby monitor. Having greater control of the bits means a more secure system than open broadcast video and audio or off the shelf IoT.
The first version is just the phone running Plumble. On the phone I have turned the volume down so no audio can sneak out from the device and disturb a sleeping baby. This connect to Mumble running in a Virtual machine.
Clients are as simple as anything that can run a Mumble client, for me it's my main Android Phone (and my wife's) and Plumble, to reduce chances of noise getting out, I have muted the microphone, but if you are regularly in a different room for you partner, you can also have a conversation, like, who's turn it is to change the baby.
I have a Pi Zero W with camera ready to go, and it will be installed soon, we'll call that Version 2.
For those concerned with security and or Google, get a cheap phone that you can get an ungoogled or AOSP image for, load up the F-droid store and download Plumble from there, or simply load the Plumble apk by hand.