ESTA and travel for non US citizen spouse

U.S. Immigration attorney here. First things first: my advice to my clients (and family, for that matter) is to always apply for the visa rather than relying on ESTA. While the ESTA program is a huge convenience when things go right, it quickly turns into a huge headache when anything goes wrong. Cancelled flights, illnesses, freak weather events, and stuff just happening can all cause you to need to extend or change the conditions of your stay, and ESTA makes that incredibly difficult to do. A traveler in the U.S. on ESTA also has significantly less rights within the immigration system than one with a valid visa. So, short answer: get the visa.

As for ESTA travel right now, the situation is fluid and inconsistent. CBP (border patrol) officers have broad discretion at points of entry, and very often they aren't well-informed about what the current state of law/policy is. That's not a dig at the officers, but rather at the system of information distribution within CBP. Some folks with ESTA are being allowed in, and some are being turned back. This is where the ESTA/visa difference comes in again - you have more ability/rights to challenge the denial of entry in a visa situation than you do with ESTA.

Standard disclaimer: I am an attorney. I am an immigration attorney. But I am not your immigration attorney, and this answer is not intended to be legal advice. It is based on my observations and experience, and you should not rely on the advice of strangers on the internet who purport to be knowledgeable (not even me). If you want solid, personalized, legal advice (and you do, you really, really do), talk to a competent lawyer directly.

I'm afraid you are misled about a couple of things.

Firstly, despite the original statement that the travel ban was for thirty days, the ban has not been lifted. It is still in place, and will probably last for months. See this article for more information.

Second, there has been no mention of preventing people from using ESTA. A Schengen Area national can continue to use the Visa Waiver Program (VWP - the real thing that people mean when they talk about "using an ESTA") to visit the US, provided you have not been in the Schengen area (or any other infected area) for at least 14 days.

As a US citizen you are allowed to travel to the US, and there are exceptions for "some immediate family members" of US citizens, according to this official webpage, so it is conceivable that your husband may be able to.

Another wrinkle in the ESTA saga: the UK FCO have changed their advice and state that

You’ll need a visa to enter the USA. The Electronic System for Travel Authorisation (ESTA) visa waiver programme is not currently in operation due to the imposition of new travel restrictions on those travelling from the UK.

However, the official ESTA web site is unchanged, and the US Embassy in London don't help!