Yes, they call themselves "empiricists" and "naturalists" which could also be applied to art, maybe. I couldn't quite make out that tannish mural posted earlier, some sort of carved table was it? Anyway as far as art's concerned the details need to be precise. I'm going out of my way here to accommodate what an empiricist might observe when visiting the Dead Sea region and will even admit Genesis as "literature" (an art) for the purpose.
Which is multiple attestations from archæologists around that area confirming by observation (eyesight) many of the details preserved in literature (Genesis) which reveal how God's historical witness is accurate concerning events surrounding the destruction of the cities of the plain.
Genesis 19:24-25 Then the LORD rained upon Sodom and upon Gomorrah brimstone and fire from the LORD out of heaven; and he overthrew those cities, and all the plain, and all the inhabitants of the cities, and that which grew upon the ground.
Empiricism observes the region. "Aha!" it says, "A region of profuse volcanic activity. How commonplace that stories about destruction exist set hereabout." Naturalism has produced those stories, not shoddy approximations but replete with details. Details revealed by the very archæologists denying Christ and holding God to be a liar.
OK. That's what we get from empiricists and their naturalistic bedfellows. Right up to the point where, however geologically active that environment may be, God reveals even more detail than they can confirm namely brimstone with fire descending from Heaven. Not so long ago there was no such thing as archæology to confirm anything. The Bible was accurate. Later, when excavations reveal ruined buildings from antiquity
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.confirming Genesis
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.The Bible remained accurate. A century or two pass, more digs and particularly in the middle east, more detail confirmed. The Bible is still accurate even up to the rapid descent of ash such as confirmed in OP with the catastrophic effect on heads confirmed. Then all of a sudden The Bible is rejected by these freaks just because there's a spiritual dimension involved which empiricism can no more confirm (yet) that it could confirm anything on this topic even two hundred years ago!
Cherry picking of the worst kind. Your husband is very wise to insist on a Scripturally based homeschool syllabus for his children.