Is the pollution from a highway next to our house making my family unhealthy?

Possibly. Over time this exposure can lead to health problems if coupled with unhealthy habits. Therefore your family should maintain a healthy lifestyle including a healthy diet, pure water, exercise and positive mental attitude.
Possibly. Exhaust exposure is not healthy. However, the problems it causes are very different in different people (none to severe), depending on how much they are exposed (living right next to a 6 lane freeway vs just near a country road), how often they are exposed, and what their underlying lung problems may be. Exhaust is a trigger to make asthma hard to control. The damage usually matches the symptoms.