If the husband is Egyptian and the wife is an Australian and Thai dual citizen, can our child hold these three citizenships?
In principle, this may be possible, with caveats.
From Egyptian nationality law:
Therefore, even if the child [born abroad] is registered with the Egyptian authorities and given an Egyptian birth certificate (proof of Egyptian citizenship), it is unclear whether Egypt would recognize the foreign citizenship at all in official contexts.
With effect from 4 April 2002, there are no restrictions (under Australian law) on Australians holding the citizenship of another country.
From Thai nationality law:
Persons born anywhere in the world to at least one parent with Thai citizenship themselves are entitled to Thai citizenship at birth.
The paperwork to establish citizenship with three different countries may be a lot of work as a practical matter (not to mention the possible costs). You will probably need to get certified translations of the birth certificate, because each of your countries have different official languages. There may be other bureaucratic hurdles to overcome too.
My own kids both have three citizenships, and I didn't get them all sorted out until the oldest one was almost 5. I still had to get certified translations, because even though all three citizenships are English-speaking, one of them was born in China (and has a Chinese birth certificate).