De asielhond is rustig, behalve dat hij soms binnen blaft.

Asielhond is a compound noun: asiel + hond.

In this context, asiel means an animal shelter, not political asylum. So asielhond means a shelter dog or rescue dog.

Dutch often makes one-word compounds like this:

• asielkat = shelter cat
• politiehond = police dog
• waakhond = guard dog

Because hond is a de-word, so the whole compound is also a de-word: de asielhond.

In Dutch compounds, the article is determined by the last part of the word. Since de hond is correct, you also get:

• de asielhond
• de politiehond
• de huishond

This is something learners usually just have to memorize with the noun.

Because rustig comes after is, so it is being used as a predicate adjective. Predicate adjectives do not take the -e ending.

• De asielhond is rustig. = predicate adjective
• De rustige asielhond = adjective before the noun

So:

• after zijn / worden / blijven etc. → usually rustig
• before a noun → often rustige

Behalve dat means except that.

It introduces a full clause, not just a noun or short phrase.

Compare:

• behalve de hond = except the dog
• behalve hem = except him
• behalve dat hij soms binnen blaft = except that he sometimes barks indoors

So behalve by itself can be followed by a noun or pronoun, but behalve dat is used when a whole clause follows.

Because dat introduces a subordinate clause, and in Dutch subordinate clauses the conjugated verb usually goes to the end.

Main clause:

• Hij blaft soms binnen.

Subordinate clause:

• ... dat hij soms binnen blaft.

That final position of blaft is one of the most important Dutch word order patterns to learn.

Here binnen means inside / indoors.

So binnen blaft means barks inside or barks indoors.

It is an adverb of place. It is not the same as naar binnen, which means to the inside / indoors with movement.

Compare:

• De hond blaft binnen. = The dog barks indoors.
• De hond loopt naar binnen. = The dog walks inside / goes indoors.

Because the subject is hij, which is third person singular, so the present tense form is blaft.

The infinitive is blaffen.
Present tense:

• ik blaf
• jij blaft
• hij blaft
• wij blaffen

So in this sentence:

• hij ... blaft

Yes, soms can move, but some positions sound more natural than others.

In this sentence, dat hij soms binnen blaft is very natural.
It places soms after the subject inside the subordinate clause.

You may also see:

• Soms blaft hij binnen.
• Hij blaft soms binnen.

These all mean roughly the same thing, but the rhythm and emphasis can change a little. For a learner, subject + soms + other information + verb is a very safe pattern in subordinate clauses.

Dutch commonly uses hij or zij for animals, especially pets or animals seen as individuals.

So using hij for a dog is completely normal. In practice:

• if the dog is male, hij is literal
• sometimes hij is also used more generally for an animal being talked about as an individual

English learners sometimes expect it, but Dutch more often uses personal pronouns for animals than English does.

Not exactly.

Maar means but, and it simply connects two ideas:

• De asielhond is rustig, maar hij blaft soms binnen.

Behalve dat means something more like except that and presents the second part as a qualification or small exception to the first statement:

• De asielhond is rustig, behalve dat hij soms binnen blaft.

So this version suggests:

• overall the dog is calm
• there is just one notable exception

The comma helps separate the main statement from the extra clause that adds an exception.

• De asielhond is rustig, behalve dat hij soms binnen blaft.

This punctuation is natural and standard in a sentence like this. It makes the sentence easier to read and shows that the second part is an added comment qualifying the first part.