In the past, several airlines have made these types of awards. In fact, I once flew from San Francisco to Chicago, from Miami to New York, and back to San Francisco for an international trip for less than $ 100 (most of which were taxes). However, I am not aware of any US carriers that have such prices today – at least not at cheaper rates (eg you will still find this as part of the world tariff, but not the usual round-trip tariffs)).
However, sometimes you can benefit from booking your domestic flights with the same ticket as your international flights.
Fares are a complex beast, but for most airlines today, flights are made by origin, destination and possibly one or more stopovers. The prices for this part of the flight also depend on each of these things – and not necessarily in a way that may make sense to you.
Suppose you wanted to fly from Amsterdam to New York and then from New York to Chicago.
There are two ways to book flights. One is as two separate flights (AMS-NYC, NYC-> CHI). The second is a SINGLE flight with stopover (AMS-CHI with stopover in NYC). Whichever is cheaper depends on the fares at the time of booking. It may be cheaper to book a one-way stopover or two flights.
Let's say AMS-NYC would cost you $ 500. And AMS-CHI with a stopover in NYC costs $ 550, while a separate NYC-CHI flight costs $ 150.
If you book the flights together and offer them as a single trip with connection to the price, you have saved $ 100. Sometimes the price can even go down if you add the extra leg – it costs $ 500 for a NYC flight, but only $ 400 for AMS-CHI (even with a stopover).
Of course, it's just as likely that it costs more to book it as a stopover. In this case, with a good booking engine, you get the cheapest combination of flights (one stop or two trips) – but sometimes airlines set rules to prevent this.
The other advantage of booking both international flights and domestic flights together is that you get the international baggage allowance (which is usually better than domestic) for the entire trip. Depending on the airlines involved, this can lead to significant savings on baggage charges.