Yes, but including more than one of either type requires multiple research questions.
For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.
You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable.
To ensure the internal validity of an experiment, you should only change one independent variable at a time.