You can find schematics in the data sheets. You just need to know where to look. I've listed some devices that look suitable further down in this post. But I want you to understand what you need, so you can be sure these devices will do what you want.
You have a requirement to be able to drive the motor in either direction for an arbitrarily long time - seconds, at least. This seems pretty obvious, but there are many drivers that can't do this. The reason is in how the positive bias voltage for the high-side MOSFETs is generated.
If you use two P-channel MOSFETs and two N-channel MOSFETs, like the design you posted in post #1, this is not an issue, because both MOSFETs can be driven by signals that range from 0V to 12V, which can be generated easily.
But if you want the best performance from your MOSFETs (i.e. high current capability, and low loss voltage and therefore minimal heatsinking requirement), it's best to use all N-channel MOSFETs, because they're just better than P-channel MOSFETs. But that requires an extra supply voltage, called the boost or bootstrap voltage, about 10V higher than the positive supply voltage, to provide the voltage needed for the gates on the high-side MOSFETs (the top two).
This voltage has to be generated somehow if you're going to use N-channel MOSFETs.
A common way to generate it is using "bootstrap capacitors" that are connected to the outputs of the H-bridge. They store a charge, and provide power for the high-side MOSFET driving circuitry. But they disharge after a short time. So both sides of the H-bridge need to be changing state fairly quickly. In many designs this already happens, because PWM (pulse width modulation) is used to give exact control of the motor speed. PWM drives the moto with a voltage that alternates between 0V and full voltage, usually at least 100 times per second, with a
duty cycle that determines how fast the motor will run.
If you want a simple forwards/backwards control without PWM, you can't use these drivers that rely on bootstrap capacitors connected to the H-bridge outputs. In this case, you're forced to use a PMOS/NMOS H-bridge, unless the boost/bootstrap voltage is generated independently. There are a couple of devices listed below that actually do this. So they have the advantages of an all-NMOS H-bridge without needing PWM.
You actually have quite a few choices.
The Microchip TC4469 (
http://www.digikey.com/product-detail/en/TC4469CPD/TC4469CPD-ND/115363 USD 3) will drive your existing two P-channel and two N-channel MOSFETs. It includes logic to prevent cross-conduction (shoot-through). The data sheet includes a schematic that shows how they should be connected.
The rest of these devices have built-in MOSFETs. This makes them a bit more expensive, but they're compact and easy-to-use.
The Allegro A4950 (
http://www.digikey.com/product-detail/en/A4950KLJTR-T/620-1470-1-ND/3305807 USD 4) is a complete full H-bridge in a little SO-8 (SMT) package with a heat transfer pad. It includes a continuous boost/bootstrap generator and an all-NMOS full bridge. It's rated for 40V and 3.5A.
The Allegro UDN2998 (no longer available from Digi-Key)is an older design with two complete H-bridges, rated for 50V and 3A (not sure if that's 3A per H-bridge or 3A total). It uses transistors not MOSFETs so there is significant voltage drop. It's a 12-pin SIL package with heatsinking tab.
The Infineon BTS7960 is also not stocked by Digi-Key or Mouser, which is a shame because it's a very impressive half-bridge driver with built-in MOSFETs, designed for automotive applications. You would need two of them.
The Infineon TLE5205 (
http://www.digikey.com/product-detail/en/TLE5205-2G/TLE5205-2GINCT-ND/1557940, SMT only, USD 8) and TLE5206 (
http://www.digikey.com/product-detail/en/TLE5206-2S/TLE5206-2S-ND/128308, THT, USD 7) are full H-bridge ICs that are rated for 5A continuous. The difference seems to be in how they handle the four possible combinations of input signals.
The On Semiconductor STK681-320 (
http://www.digikey.com/product-detail/en/STK681-320/STK681-320OSCT-ND/3598311 USD 11) is rated for 5.2A.
STMicroelectronics make a range of devices with integrated MOSFETs but some of them aren't designed for continuous output (they use a bootstrap capacitor which requires that the outputs toggle regularly). You can investigate them if you want to. Start with the L6201~6208.
Texas Instruments make several motor driver ICs as well. Check out DRV8840 and DRV8842; they have built-in charge pumps that are permanently active.
If you just want a suggestion, I suggest you start with the Infineon TLE5206 (
http://www.digikey.com/product-detail/en/TLE5206-2S/TLE5206-2S-ND/128308, THT, USD 7) which is rated for 5A continuous. Study the data sheet carefully to make sure it will do what you want.