It's possible and effective, but I would recommend going for the strength using compound movements first and the more specific hypertrophy second. The primary reason for this is fatigue management. The fatigue induced by a heavy set affects the longer lighter sets less than the other way around.
Wendler 5/3/1 program is built around this approach. The strength portion is first and features 3 work sets of 1-5 reps where the top set is for as many as you can do at the programmed weight. After you do the strength work, you add in 5 sets of 10 for hypertrophy. To complete the program you would also work on mobility and conditioning.
You'll find this approach works much better with heavy compound movements used for the strength work than it does with smaller isolation type movements.
- Compound movements such as bench, squat, deadlift, pull ups, dips, all affect multiple muscle groups. Due to that fact, it is more effective at strengthening all the muscles being activated.
- Isolation movements such as curls, triceps extensions, chest flies, are best done in volume for hypertrophy affect and/or joint health.
The bottom line is that the smaller muscles used in isolation movements are only going to get so strong on their own. In order for your mind and body to agree on heavier weight, the mind has to be assured that the rest of the body can handle it. It's one reason that deadlifts are limited by what you can grip. The mind puts the breaks on if it thinks you can't hold the bar, and this is an involuntary reflex. Since compound movements take care of multiple groups of muscles, when you go back in for isolation work you will be able to do that at higher weights.
The alternative approach also works. It's similar to how Hepburn routines splits things up. Essentially for a few months you are working on strength primarily, and when you can't make any more progress that way you switch to hypertrophy for a few months. And alternate.
I personally prefer to do the strength and hypertrophy work in the same session. Both are needed to get stronger (my goals), and it's just a matter of adjusting the proportion of work that goes into what I want to emphasize at any given time.
Just an additional note: don't get hung up on just one set/rep scheme. Sometimes when you are hitting a plateau, you need to change your approach. Sometimes you need to add sets, or reps. Other times you cut the sets/reps and add weight.
A simple and effective way to balance this out is to start with a baseline set/rep scheme. It can be 3x8 for example. Just keep at the same weight and try to work up to 4x12. When you hit that, increase the weight you are using and start over with 3x8.