You can stay in contact but you need to be careful about which methods you use and what information they require you to provide.
Writing a letter is your safest option right now. Through InmateAid's letter service your personal address does not appear on the envelope, which provides a layer of privacy that direct mail does not. The letter reaches your husband without exposing your location to anyone processing the mail at the facility.
Phone calls carry more risk depending on how the system records and verifies the numbers being called. If the facility's phone carrier logs incoming numbers or requires registration, your location and identity become part of that record. That is a risk worth weighing carefully given the warrant.
Video visitation is the highest risk option. Most video visitation platforms require identity verification, account registration, and in some cases a physical address. Providing that information with an active warrant creates a direct line between you and the authorities. Avoid video visits until the warrant situation is resolved.
The most practical advice is to deal with the warrant proactively rather than waiting for it to catch up with you at the worst possible moment. An outstanding warrant does not expire and it does not disappear. Every interaction with any system connected to law enforcement carries the risk of surfacing it. An attorney can often arrange a voluntary surrender on terms that minimize the disruption, which is a far better outcome than being picked up unexpectedly while trying to stay in contact with your husband.
Resolve the warrant and all of these concerns go away at once.