Trg signal might be the same, but the signal level is not the same. To open a N-channel MOSFET you need to apply some positive voltage, say +10V, above its source. Since the source of fully opened high side MOSFET is tight to positive supply of the bridge, in your case +30V, you need to apply around +40V to the gate relative to ground. It is a way to high for your low side MOSFET, Vgs(max)=+/-20V. So you can not connect gates together.
You need also create this +40V in your circuit. IR2110 is typically used in a bootstrap configuration, where a bootstrap capacitor (connected between Vb and Vs) is charged throught bootstrap diode (connected between Vcc and Vb, see fig. on the first page of IR2110 datasheet). This is the easy way of doing it, but you get some limits on max. duty cycle of the high side switch (see datasheet and/or appnote for bootstrap calculation).