Measure white wine vinegar, lemon juice, mayonnaise, Dijon, honey, minced garlic, salt, and pepper into a bowl and whisk together thoroughly. Continue whisking while slowly adding olive oil. Taste and adjust seasonings, as desired.
Store in the refrigerator (because of mayonnaise) but allow to come to room temperature for a few minutes and shake well before serving.
Mince one clove of garlic very finely, then use a fork or the flat side of your knife to mash it. Measure out 1/2 teaspoon to add to vinaigrette.
As an alternative to whisking, you may measure all ingredients into a jar with a tight-fitting lid and shake vigorously. Or you may combine everything in a mini food processor and process until well combined.