I have been practicing martial art for a number of years, usually about 3 times a week. Recently I've come to conclusion that my fitness level (which is rather low) impedes my progress and MA training I am doing is not enough to increase my fitness, so I joined a Crossfit gym. So far I like it, but my question is how to combine Crossfit with my martial art training for best results. I have about 4 to 5 days a week that I could exercise (depending on work, family circumstances, etc.), about 1-1.5hr a day, and I would like to do at least 2 days of each MA and CF if possible. What would be the best regimen?
MA training is 1 hour (sometimes 1.5 hr) usually involves some cardio exercise which depends on the practice, partners, etc. could be from pretty easy to quite challenging, but does not require too much strength usually. The CF workouts are usually within 1 hour too and depend on WOD. So far I feel I am making some progress fitness-wise, but I am concerned that doing fitness training only 2 times a week may be too little to make good progress. Is it true and if yes, what would you advise?
If it's relevant, I'm 37 y.o. male, not very fit but healthy, somewhat overweight (BMI=27).
Update: the aspects I want to improve is primarily endurance and secondarily strength, i.e. I want to be able to do more pushups, more pullups, etc. I don't want to be a powerlifter or competing athlete, just to improve the fitness level.