A “half-and-half” pizza (also sometimes called a “split” pie) is a pizza with different toppings on each half. For example, one half could have a pepperoni topping and the other half could have mushrooms on top.
 
The origin of the first “half-and-half” pizza is not known, but it’s cited in print from at least 1953. According to the “Slice” pizza blog in 2007 (see below), some establishments charge for two toppings, even though there is only one topping on each side on a “half-and-half” pie (not including other combinations).
   
   
1 October 1953, Wisconsin State Journal (Madison, WI), “Pizza Ranks as Favorite Dish in U.S.,” section 2, pg. 3, col. 2:
A pizzeria also will make a half-and-half pie, for example, one section with mushrooms and the other with sausages.
 
11 April 1957, Hammond (IN) Times, pg. C3 ad:
frozen fresh
Jud’s Sausage, Cheese, Mushroom or Half and Half
PIZZA PIE…Each 79c
 
19 February 1960, Logansport (IN) Pharos-Tribune, pg. 16, col. 3 ad:
COMBINATION OR HALF & HALF
(Jerry’s Pizzeria—ed.)
   
Slice
Pricing on Half-and-Half Pizzas Explained
Posted by Adam Kuban, June 5, 2007 at 2:21 PM
Like most pizza lovers, I often find myself sharing a pie with one or more friends. That invariably means heating arguments over toppings. The easiest way to broker peace (at least for the moment) is to do half-and-half pies.

Pricing on, say, a half-pepperoni, half-mushroom pie seems straightforward enough. You should be charged for one topping, right?

Not always. Sometimes a place will charge you for two toppings. Why is that? Blogger Rafi Mohammed has gone through the trouble of formulating a theory:
 
In search of answers, I posed this fascinating pricing conundrum to a couple of my friends and together, we came up with a working hypothesis. Our initial research revealed that legendary and gourmet pizzerias tend to charge for two toppings while Mom & Pops and chains seem to only charge for one topping. We hypothesized there are two key reasons why legendary and gourmet pizzerias charge for two toppings. First, customers that patronize these establishments tend to be less price sensitive. This notion is supported by the fact that I rarely, if ever, see coupons for these pizzerias while discounts (coupons, volume specials) are readily available at chains and Mom & Pops. Second, customers dining at legendary and gourmet pizzerias highly value unique toppings. This concept is supported by the fact that these restaurants are often known for specialty toppings such as clams, homemade sausage, thyme roasted mushrooms, etc.
 
Although I don’t like it when I’m charged for two toppings when I’ve essentially ordered one, I think Mr. Mohammed’s theory is a sound one, and all my pizza-eating experience seems to back it up—even though I can’t think of specific examples of where I’ve been charged full price for half the topping.