The information between the pair of commas is nonrestrictive. That's why it is being set off as it is.
This is the essential sentence:
The truth is that after hospitals are hit, our houses have become hospitals.
Since the additional information is not restricting the sentence, it is inserted between a pair of parenthetical commas. It could also be removed without impacting the grammar of the sentence:
The truth is that after hospitals are hit, and in areas like this where there is just one hospital, our houses have become hospitals.
The same grammatical function could have been served with dashes or parentheses:
The truth is that after hospitals are hit —and in areas like this where there is just one hospital— our houses have become hospitals.
The truth is that after hospitals are hit (and in areas like this where there is just one hospital), our houses have become hospitals.
The use of and may be misleading in terms of parsing what's going on. Consider the same sentence with especially instead:
The truth is that after hospitals are hit, especially in areas like this where there is just one hospital, our houses have become hospitals.
To answer a comment, this cannot be an independent clause followed by two dependent clauses.
The comment said:
The truth is that our houses have become hospitals.
That sounds fine. However, it's not what the sentence says.
What it does say is, on its own, ungrammatical; therefore, it's not an independent clause:
✘ The truth is that after hospitals are hit.
There is no completion:
? The truth is that after hospitals are hit … What? What is the truth?
This, too, is not meaningful:
✘ The truth is that after hospitals are hit, and in areas like this where there is just one hospital.
It has the same problem as just the first part of the sentence does.
? The truth is that after hospitals are hit, and in areas like this where there is just one hospital … What? What is the truth?
No single part of the sentence stands on its own because of the use of the word after. If after were removed, then the first part of the sentence would be an independent clause.
While you could argue that our houses have become hospitals is an independent clause, if that were the case, then the way the sentence as a whole is phrased would not work. You couldn't say that everything that comes before it is simply introductory. It would make sense if it stood on its own—but it doesn't make sense as part of the greater sentence when interpreted in that way.
The only meaningful independent clause that stands on its own as a complete thought, and as part of the whole sentence in context, is the simplified version that I gave at the start of this answer:
The truth is that after hospitals are hit, our houses have become hospitals.
In the full sentence, the portion of the sentence after the second comma completes the thought and clause from the portion before the first comma. Without that it would not be a meaningful sentence.
This is a single independent clause. It's the only form of the sentence that stands on it's own in a meaningful way.
In the full version, this independent clause is interrupted by a dependent clause that is placed in the middle, between a comma pair.