Let's spend some time on this choice for the high-side elements. As said before, N-channel devices would be desirable for this role for their lower losses, but there's a problem: for them to operate properly, their source must be connected to the motor leads and their drain to the power rail. When a P-channel device is used, its source will be connected to the power rail and its drain to the motor leads. Now, the problem is that both devices are controlled by their gate-source voltages. For P-channel devices it means that if the gate is connected to the power supply, the device will be closed (gate-source voltage is 0) and if the gate is grounded the device is opened (provided the power-supply is actually enough to open the device), since gate-source voltage is equal to the power supply voltage.For an N-channel device however the picture is more complicated. If you connect the gate to ground or to source, the device is closed (gate-source voltage is below or equal to 0). But where to connect it to open the device? The power supply is not enough, since, when the device is open, it's source and drain are roughly at the same potential. Since the drain is connected to power, the source will be at that potential as well, but than gate should be higher than that to keep the device open. In fact at minimum 5V higher for so-called logic-level MOSFETs and 10-15V higher for normal MOSFETs. This is a significant problem, that voltage somehow has to be generated. In most cases some kind of a charge-pump is used for that, either in a stand-alone or a boot-strapped configuration. The latter however is only useful if the bridge is driven in the 'locked anti-phase' mode (see later). In any case, these high-side drivers usually cannot deliver as much current as a regular low-side driver can, which means longer turn-on and -off times for the high-side (lower current takes longer to charge-discharge the gate-capacitance). In high-frequency operation, where switching loss is a significant factor, a P-channel MOSFET might be a better solution because of this. In low-frequency, high-current operation, where switching loss is not a problem, but channel-resistance is, N-channel transistors are usually a better compromise.
So if I tried to use all N types, I wouldn't be able to turn on any of the high sides using that driver? If you're saying the gate voltage is relative to the source of the mosfet, what gate voltage would be required, given that the source of the highside is connected to the drain of the low side?
Why not just use the arduino to drive 4 pins in various configurations?