هذا بيت جميل.

هذا is a demonstrative pronoun meaning “this” (for masculine singular nouns in Modern Standard Arabic). In this sentence it functions as the subject of a nominal sentence (a sentence without a verb), often analyzed as:

• هذا = مبتدأ (mubtadaʾ, “topic/subject”)
• بيت جميل = خبر (khabar, “comment/predicate”)

Because بيت (house) is grammatically masculine in Arabic.

• هذا = “this” (masculine singular)
• هذه = “this” (feminine singular)

Even if the real-world object has no biological gender, Arabic nouns still have grammatical gender, and بيت is masculine.

In the present tense, Arabic typically does not use an explicit “to be” verb in nominal sentences. The meaning “is” is understood:

• هذا بيت جميل = “This (is) a beautiful house.”

If you wanted past tense, Arabic would use كان:

• كان هذا بيتًا جميلًا = “This was a beautiful house.”

Arabic doesn’t have an indefinite article like “a/an.” Indefiniteness is usually shown by: 1) No ال- prefix, and often
2) Tanwīn (nunation) in fully vowelled text: بيتٌ جميلٌ

So:

• بيت (often: بيتٌ) = “a house”
• البيت = “the house”

In fully vowelled MSA, yes, you would commonly see:

• هذا بيتٌ جميلٌ

Both بيتٌ and جميلٌ are indefinite and (in this structure) typically nominative, so they take ـٌ (ḍamma + tanwīn).
In most everyday writing, short vowels and tanwīn are omitted, so هذا بيت جميل is normal.

It’s a nominal sentence. A common analysis is:

• هذا = subject/topic (مبتدأ)
• بيتٌ = first part of the predicate (خبر)
• جميلٌ = adjective describing بيت

So the predicate is essentially “(a) beautiful house.”

In Arabic, adjectives usually follow the noun they describe.
So:

• بيت جميل = “a beautiful house” (literally “house beautiful”)

This is the normal order in MSA.

Several clues point to it being an adjective: 1) Position: adjectives normally come after the noun.
2) Agreement: an adjective agrees with its noun in gender, number, case, and definiteness. Here:

• بيت is masculine singular and (typically) nominative/indefinite
• جميل matches that: masculine singular and (typically) nominative/indefinite

You would make the noun definite with الـ, and the adjective must also become definite:

• هذا البيت الجميل = “This is the beautiful house.”

In Arabic, the adjective must match the noun in definiteness.

A common pronunciation (without case endings) is:

• hādhā bayt jamīl

With full case endings (more formal/fully vowelled):

• hādhā baytun jamīlun

Notes:

• ذ is like the th in “this” (voiced “th”).
• jamīl has a long ī sound.