Until only recently I was either using only natural or only artificial light (speedlight or strobes) in one picture at the same time. However, rules are meant to be broken (yes, it was a very weird rule I had to use only one type of light during a shoot) and lately I've been combining and mixing natural and artificial lights. I really like to use one type of light as a hair light and the second as a fill light or as the main light.
I particularly like to use natural light as a hair light for several reasons. Firstly, if I use a speedlight as the main light, then I have much more control over the light, its strength, position and I can apply light modifiers onto the speedlight. Secondly, if I have to shoot at noon when the natural light is not too flattering (yes, sometimes I just had to shoot at noon when it's the only option for a model, a make-up artist and a stylist), using the natural light as the hair-light is the best option. Thirdly, having the sun behind the model and sometimes having it in the frame and then compensating the exposure with the speedlight can give some nice and creative results.