- agreement: if a noun has a given article, so does any adjective modifying it. Thus "a short boy" in Arabic is walad-u-n qaSiir-u-n (where -n marks indefiniteness, and -u marks the nominative case), whereas "the short boy" is al-walad-u l-qaSiir-u. (The vowel of al- elides when preceded by another vowel.)
- In direct compounds of two nouns (possessed-possessor, or more generally modifier-modified), the first noun cannot take any article. Thus in Arabic you can say yad-u l-walad-i "the boy's hand" or yad-u walad-i-n "a boy's hand" (-i marks the genitive case) but not *al-yad-u l-walad (intended to be "the hand of the boy") or *yadun al-walad (intended to be "a hand of the boy").
The second property isn't actually all that "exotic" - English does the same thing! You can say the man's hat, but never *the man's the hat or *the man's a hat; just as in Arabic or Hebrew, to make the full range of possible definiteness distinctions you have to resort to prepositions.
Definiteness agreement between nouns and adjectives is more unusual, but at least one Indo-European language has it: Norwegian. No question of substratum influence there, certainly... Anyone have another example?
However, in determining whether or not the article represents a shared innovation, the question is whether other relatives have it. I recall that Biblical/Imperial Aramaic did (later varieties lost it), but I'm not sure of the detailed behavior of its definite article. The Berber obligatory noun prefixes probably derive from an original article (see my post Beja and Beyond) but, though distinctly similar to the Beja definite article, don't seem directly comparable to the Arabic and Hebrew ones.