There are a number private medical and dental clinics in Beijing. The most established foreign owned private hospital is United Family Hospital. They offer both in and out-patient treatment and have specialists in a number of fields.
Some of the other private clinics in the city are:
Peking Union is Beijing's, if not China's, most prestigious university hospital. In fact, many of the private clinics' specialists are based at this hospital. There is a private section (which means you don't have to join the very large queues for consultations). Even here, the rates are significantly less than at the private clinics. However, even if you schedule a consultation, you'll probably have to wait. Some of the country's top doctors are here, but the administrative systems aren't for patients in a rush.
An outpatient consultation at a private clinic costs up to USD100. A birth at a private hospital (excluding pre & post natal consultations) costs about USD25,000. It is highly recommended that you have medical insurance before relocating to Beijing. It's also advisable that you have evacuation coverage. An evacuation to Hong Kong (or further afield) from a location in mainland China can cost up to USD50,000. Note that some clinics have direct billing arrangements with insurers. You ensure also that prior to arrival your family has the recommended vaccinations.