Perhaps what you're looking for is something that smashes the two worlds of cardio and weightlifting together in one. In the Crossfit world, this is a Metcon. I know it as Circuit Training.
Circuit training is basically doing a series of related workouts in a specific order. You don't do them with particularly heavy weight because the point is to just keep going from one workout to another. The total workout lasts maybe 20-30 minutes, and various plans typically include both weight lifting and cardio. Though despite the length, it is a very intense workout! If you aren't sweating by the end of it, then you simply didn't go hard enough. Though always be cautious that form doesn't break down. It is common for people to get a little carried away and walk out with an injury.
There are a growing crop of gyms (at least in the United States) like Orange Theory which do these kind of workout. They only do classes which makes them cheaper than hiring a personal trainer for yourself. There are other gyms that advertise them as "boot camp" style classes. There is of course also Crossfit, but I find them to be really expensive.
If you'd prefer your own, you can just search "circuit training programs" or "Boot camp workout" and you'll find all sorts. They can be rather difficult to do in a gym, however. If you do them in a commercial gym, then you have to be courteous of the other members. You don't want to be "that guy" that takes up all the equipment to complete their circuit. Though if you can find a good spot to do it, then go for it.
