If he is your spouse, i.e. married or in a registered same sex partnership, then it would be easier for your new employer to do the paperwork for you both. He would then have a dependent's L permit and could look for work. There are certain conditions any employer would need to meet however:
Point 4.4.1 of the Foreign Nationals Act says
The employer must ask for authorization
The salary and work conditions should be "correct"
Also, the members of the family must have professional qualifications
Whether that means an employer would also have to prove they can't find a Swiss/EU national who could do the job is under debate here on the forum. Dependent Work Permit - Non EU
It has been done fairly often so I don't think it is that much of a problem. The main one I can see is exactly what do you mean by "global health"? If he's looking to work for pharmaceutical companies for example then that could be possible, but if it's more "mundane" and we're talking about working in a hospital then he'd need a good level of fluency in a Swiss language; for Zurich that would be German.
He would not be able to apply for a permit himself, non-EU nationals can only be hired once any job offer has been approved by the Swiss authorities as outlined here: https://www.bfm.admin.ch/bfm/en/home...zulassung.html
The only ways he can get a permit is either as your dependent or via an approved job offer of his own.