A couple things could be causing this. I've only ever seen this sort of waveform when using a gate-drive transformer(not enough drive power) though, so keep that in mind when reading my post. At a slower speed of 20kHz, 100nF for your bootstrap capacitor seems very small to me, to be able to provide drive power to the high-side FET for that long of a period([50uS/2] - 1.2uS(dead-time) = 23.8uS). I'm assuming that the image of your waveform is 5V/div, so close to 15V drive voltage seems fine. I know when using an IR2110 @ ~25kHz I used bootstrap caps from 1uF up to 10uF depending on the dead-time and maximum duty cycle. It is also recommended that you place a cap that is 10x(so 10-100uF) the value of your bootstrap cap across VCC/Gnd to aid in charging the bootstrap cap faster during the time that Vs is pulled low. This is in addition to the normal low value bypass cap that would be across VCC/Gnd. Also, that BA159 seems to have a fairly slow Trr(Reverse-Recovery Time) of 500nS when compared with the rise-time of the IR2153 outputs(Typically 80nS, although the rise-time at the Vs node would be slower due to the switching time of the FETs), and could be leaking current spikes back into the VCC supply causing problems(this is only speculation). I usually use either a BYV26C(600V/30nS) or BYV26E(1000V/75nS) diode to provide the bootstrap current.
Finally, you are correct that both driver outputs(LO and HO) should have very similar wave shapes. I think what MicrosiM was getting at with his question was; where exactly are you probing your circuit when you measured that waveform? I know you said that this is the waveform for the LO drive of the IR2153, but are you connecting your probe directly at the pins of the IC(across LO and Gnd) or are you connecting the probe across G-S of the FET? Depending on the length of the PCB traces between the IC and the FET and the components you may have placed along that path(gate resistor, reverse diode to accelerate turn-off of the FETs, ect.), the waveforms can be different depending on the probing location. Also, you said that the waveform on the HO gate drive is a total mess. How are you probing that? Are you probing it properly using an adequate differential probe or are you probing it by some other means such as a 100x probe, or two channels with 100x probes and subtracting the channels with the Add/Invert function of the scope. How long is your ground lead on your scope probe? Long ground lead length mostly causes problems when probing much higher frequency signals, but it can also cause problems when probing signals with fast rise/fall times as well.