Melt white baking bar; cool. In a heavy large saucepan combine the half-and-half or light cream and sugar. Cook and stir over medium heat just until sugar is dissolved.
Gradually stir about 1 cup of the warm mixture into beaten egg yolks. Return all of the egg yolk mixture to the saucepan. Bring to a gentle boil, stirring constantly. Remove from heat.
Stir melted white baking bar into the egg yolk mixture until combined. Stir in whipping cream and vanilla. Cool thoroughly by placing the saucepan in a sink of ice water or chill overnight in the refrigerator.
Stir milk chocolate and semisweet chocolate into the egg yolk mixture. Freeze in a 4- or 5-quart ice cream freezer according to the manufacturers directions. Ripen 4 hours. Makes about 16 servings (about 2 quarts).