Depends on the year, make and model. Pre-1968 US cars were generally wired to shut the parking lights off when the headlights were on, with few exceptions. This is the normal operation. If it really bugs you, you can jump a wire between the tail light and front parking light lines.
Brake lights should NOT be effected by the headlights. Brake light function is completely independent of the headlights. Assuming you are not refering to the tail lights, or marker lights, which are supposed to come when the head lights are turned on. Not having brake lights when the head lights are on is a big safety problem and should be corrected.
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