Sony recently developed a new type of camera, the Single-Lens Translucent brand, that features a semi transparent fixed mirror. The mirror lets most of the light through to the sensor, and does not move for taking a picture, while redirecting some of the light up to a separate phase detect autofocus sensor. This allows for live view with fast phase detect autofocus, which is great for regular video and quick shots.
The system can be used quite well for infrared and has some benefits and drawbacks.
Firstly, the camera only composes through live view, so on a converted camera you can see and compose directly in infrared using the LCD or viewfinder. Unfortunately, the camera's main benefit, the use of a phase detect autofocus sensor, is a drawback for infrared use. While using this separate sensor is quicker than using the primary sensor for focusing, it will still focus using visible light. As a result, it will perform much like a traditional DSLR for infrared use and can have inaccurate infrared focus. If you are unfamiliar with why this causes focus problems, you can read up on it here.
When converted to a dedicated infrared camera, the focus can be calibrated to a particular lens like on a DSLR. The camera will then act essentially like a mirrorless camera, letting you compose in infrared. Different lenses may focus less accurately than others, just like on a traditional DSLR, but most will be close.
When converted to full spectrum and paired with external filters, focusing can get interesting. The AF will be calibrated to visible light, so when using an IR filter the autofocus will be off. Unlike DSLRs with live view, you can't force the camera to use contrast detect for this kind of use. Fortunately, even with the IR filter on the lens, the camera's live view display will show the scene in infrared on the LCD and viewfinder. This allows the camera to be used for manual focusing intuitively with any filter on the lens. Shooting with visible light these cameras will focus normally.
Below, a sample from an A55, full spectrum converted, manually focused with a 720nm filter.