International schools can be found in just about every major city outside the United States. These are schools which offer instruction in English as well as the usual kind of college preparatory curriculum you'd expect to find in an American high school, public or private. Advanced Placement courses or International Baccalaureate programs will generally be available.
In many major cities which have a lot of Americans you will even find so-called American schools. Your children will almost feel as though you never left home. Whether you choose to expose your children to a true international school with children from all over the world as well as a few local children or decide that sticking with an American school is best is a decision you will have to make based on what you feel is best for your children.
There are several sites you can use to research schools. For example, using our hypothetical transfer to Berlin, a search of the Council on International Schools' site shows four schools in Berlin. I mention this simply so that you can see that schools are available. Your company's HR department will have all the facts and information ready for you to help you find the best school for you in your new city. They have handled expat employees before, so they know what they are doing.
What about moving the children in the middle of an academic year? It's not easy, to be sure, but it's done all the time. Moreover, most international schools abroad are accustomed to accepting expat students in the middle of a year. This assumes that your children are not juniors or seniors. If they are, then you have another option. Consider putting them in boarding school if possible. In other words, you might want to leave them back here in the States.
On the other hand if you 'sell' the move as a great, once in a lifetime adventure with the opportunity to live in a different country, the chance to visit other countries in the area, and all that sort of thing, you might be able to convince your teenager that the move will be worth accepting. Europe, for example, has enough nooks and crannies to explore to keep him busy for years. If he skis, can you imagine the fun he will have skiing in the Alps? Will he miss his friends? Sure. But he will have the opportunity to make more friends overseas.
If you have primary school aged children, the move will probably be a bit easier than with older children. There are plenty of excellent Montessori and Waldorf schools overseas. Your local HR department will have a list of schools which have passed muster. Basically it will just be a matter of choosing the style of teaching you prefer.
Transportation and Security
As you begin to think things through, you will probably wonder about security issues in a major metropolitan area in a foreign country. The school will have a transportation service which it can recommend to you. Again, your local HR department will have transportation and security under control. Be alert. Be aware. Teach your children to do likewise.
Living abroad with school-aged children is indeed an adventure. But if you do your homework and understand what you are getting into, both pluses and negatives, it will be a terrific experience. My late wife was posted overseas as general manager of a bank in The Bahamas. (I remember not even knowing where the Bahamas was!) We had an amazing time. Our youngest daughter went to a private school there and did well. Good luck!