It really depends on your goals. Are you a body builder? Are you training for health or fitness? If you are a bodybuilder it is more common to train push muscle together (chest and triceps for example) and pull muscles together (lats and biceps), rather than biceps and triceps together. That does not mean what your are doing is wrong. You should probably add some core type movements such as planks and medicine ball chops as well.
If you are training for health and fitness I would encourage you to focus more on training body movements rather than individual body parts. You should also be doing some form of cardio at least three days a week.
To be honest with you, there is really no correct answer to your question. The reason is simple: it depends on the person, their genetics, their diet, their training regiment/program, their resting/recovery time and more important their mind. For this reason, you need to find out what works best for you and stay on that routine. If the routine you have described is working for you then keep it as is, if not switch to a different one. You could switch the days of one muscle group with another one or add one more group to a particular day or take more days off or even switch your diet. I know this sounds complicated, but only you can find the right recipe that works for you.
To answer that question it would help to know what fitness goals you are trying to achieve.
If your current strength training program is working for you then continue. I would also add a component of cardio to your program a few days a week for added health benefits.
Again, it depends on your specific goals as to whether or not this program is good.