There are exceptions to this for different dragon types. In addition all half-dragons have a special immunity towards the element of their breath weapon.

Silver and White dragons blow extremely frigid air and ice. Black, Green and Copper exhale acid and corrosive gas. All Half-Dragons have a breath weapon according to their variety. When engaged in combat Half-Dragons are formidable creatures and can be nearly invulnerable to weak adventurers. Half-dragon's features are reptilian, with scales, horns, elongated faces and exaggerated teeth and claws. Metallic half-dragons are usually kind except when abused by the common races in the game which will turn half-dragons away from all others except from its kin those based on evil chromatic dragons often mirror their progenitor's outlook. This sort of conception usually happens when a dragon has been polymorphed or had its form changed in some way. A dragon's magical nature allows it to breed with virtually any species.

Half-Dragon is a fictional creature from the Dungeons & Dragons roleplaying game. Source= Monster Manual, Draconomicon, Races of the Dragon Alignment= Varies due to dragon parent's alignment

Half dragon player character