I'm part of an exercise forum and this is one of our most debated topics. Some argue you should do weights first for a better cal burn, some say cardio first to warm up the muscles, or as Jess said do them in circuit.
Bottom line is do what you like and what you feel works for you. Do a week of weights first, then a week of cardio first, try a week of splitting the workouts, and a week of doing them together circuit style. Take notes and see how you feel afterwards, if you have lost weight, gained strength or if you split the workouts, which you like better and enjoy the most with the least dread factor.
Today I did two 45min weight workouts about 2hrs apart. I used heavier weights and enjoyed the second workout more, plus burned an additional 301 cals over the first workout. Was it because I split the workouts or because I just worked harder the second time???
Guess I'll have to try it again to find out.
hope that helps