One of the biggest problems with using shoot-through umbrellas is that they can blast light all over the shooting area; you get light going through the umbrella, and you also get light bouncing off of the inner curve of the umbrella, and that light causes what is called "ambient spill light". The ambient spill light from a shoot-through umbrella can, in many rooms with low ceilings or smaller-sized rooms, raise up the overall lighting in the room, thus creating a lot of fairly well-lit areas behind the main subject.
One of the things about umbrellas is that they tend to light up a fairly broad swath of real estate; in some situations, that makes umbrellas produce rather dull, flat lighting. The light going through a shoot-through can create a main light effect, and in some rooms, the ambient spill lighting creates what is, for all intents and purposes, fill lighting. At times, the fill created can be strong enough that the lighting effect is somewhat dull and uninteresting.
One way to counteract this is to use a reflecting umbrella, which sends basically all of the light out, in one direction, not half forward and half to the rear. Or, use an enclosed umbrellas, like the Lastolite Umbrella Box, or the Photek softlighter, which both perform more like a softbox than an umbrella. Or, use a softbox. Or, use a larger-sized parabolic reflector, like a 16 to 22-inch reflector. Or use a beauty dish, either with or without a grid and or diffuser cap. Or, use a softbox. A softbox with a recessed face will help eliminate backdrop light-up, and a softbopx with an egg crate grid will help keep the light mostly confined to the areas right in front of the softbox, and will minimize spread of light to the background.
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