Hi OP!
If your husband had been in finance/IT or some such occupation, I would have suggested Switzerland, since you are both fluent in French and German (what level of fluency are you btw? B2, C1, C2? Can you prove it?). Often English is ok for these jobs, but life is a lot easier there if you speak, read and write the local language (which in the German speaking part is actually Swiss German spoken and High German written), and necessary for dealing with local authorities/tax authority/medical visits etc. However, I do not think it is easy if you are going into a medical role. He would need at least C1, but more likely C2 (well educated native) level of German or French. He would also need to have his qualifications recognised and possibly need to pass extra exams which takes time and money. Also, is there a shortage of his speciality? The same will be the case in most countries for anyone practicing medicine.
Switzerland is a great country to raise children, but can be a bit boring unless you are very outdoorsy/sporty. In the Swiss German speaking part (of which I have extensive experience), the people are very very slow to warm to you, so unless you are happy to be stuck in an expat bubble (and quietly disliked for it by many locals) it's best to integrate asap - this could still take a while. However, if you're both keen to get involved in community stuff, there's lots of sports clubs and other societies that are desperate for people to help run them (this has gotten worse in the last 20 years or so, since the one earner model is also no longer possible except for the richest, so working age people have less time to spare than previously, so that's a good way in. So between fewer SAHMs (and it used to be always mothers, and still is to a very great degree), and longer acceptable commutes, this unifying aspect of Swiss communities (think all important Turnverein etc) is on shakier foundations nowadays.
A big downside is that you could be financially worse off. Renting in the areas with most jobs (but this might be different if you are going to work in a hospital in a less economically wealthy part of the country) makes the pips squeak! If you have no capital/savings, then you will not yet be in a position to buy. Even cheaper parts of the country are expensive by UK standards. Also the pound has lost a lot against the Swiss Franc in the past 5+ years, so GBP savings won't go as far there. If you were planning on putting your kids into the generally good local schools, this might actually be ok. If you plan to continue with private schooling, I do not think you are well off enough tbh. Switzerland also (still) has household based taxation for married couples, which is disadvantageous when both partners work - to the extent that we have friends who had a wedding party but did not get married! I still feel miffed that I paid out for a posh hotel stay and gift and travelled with a young baby but that they then chose not to make it official to save some tax - especially since I had to pay the tax!
How many children do you have? What age are they? Are they fluent in a language other than English? What is their ALN? We actually moved back to the UK from Switzerland some years ago. I know, mad! My DH wanted to move here, and it was the best time with DC age in mind. It became apparent that DC has ALN (ND), and while it has been a major battle to get diagnosis, identify needs, try to get them met (mainstream LA school), we are getting somewhere now. When the battle seemed insurmountable, we looked into moving back to Switzerland (or somewhere else better served in the UK), but realised they were very far behind UK on this sort of thing, and found similar to be true of Germany as well. The education system in Switzerland is excellent if you have standard issue kids, but woe betide you if you don't! Also remember that as things stand, if you intend for your DC to attend uni in the UK, you will be liable for overseas fees (and no loan) unless they have been uk resident for 3 years prior to enrollment. That's a lot of cash to come up with if you are capital poor.
May I suggest an alternative way to solve your COL/safety concerns? Why don't you stay in England, but move to a much cheaper and safer area? Many rural/economically deprived areas are desperate for medical specialist. It's certainly true where I live. If you could get work too, it might be possible for your DH to put the part of his salary over £100k into pension, and as long as you are paid under £100k (or put what's over into pension) you could get a certain amount of free childcare - if this is what's making it difficult for you to be employed (this works in England, but not Wales, where criteria is £100k gross not net). There are plenty of really lovely places to live in England outside the S.E., so why not choose one of those?
I also lived long term in East Asia, and it is a very different world. The language challenges are also at another level for most people. I speak/read/write the language of where I lived, but I stood out like a sore thumb, and that never goes away. It was a wonderful experience, but I would not have wanted to do it with DC for many reasons including the effect of pollution on development.
I am happy to discuss further if you wish to PM me.