"I love my husband."
Translation:Я люблю своего мужа.
It's just a quirk of Russian language, when referencing an object of the sentence which shares ownership with the subject of the sentence to use Свой/своя/свое rather than Мой/Моя/Мое/Твой/твоя/твое/его/ее etc.
It's kind of like replace "my" with "ones"... я люблю себя - I love ones self
You can however use the personal to really emphasize ownership
I love my girlfriend я люблю свою девушку
I love MY girlfriend я люблю мою девушку
However when referring to a third person, you absolutely should use свой.. to avoid this confusion...
She loves her (own) husband Она любит своего мужа
She loves her (someone elses) husband Она любит ее мужа
To put it as simple as possible, I'll use an example with the feminine noun Утка (Duck)
-- Nominative case = The word in the sentence that is the one doing something
Duck is sleeping - Утка спит
-- Accusative case (Утка - Утку) = The word in the sentence that something is happening to
I am eating a duck - я ем утку
-- Genitive Case (Утка - Утки) = This one is a complicated case but in general it's the word in the sentence that could be proceeded by the word "of..."
I am eating a plate of duck - я ем тарелку уткы
-- Dative Case (Утка - Утке) = The word in the sentence which receives something, in general think of it being the word in the sentence that could be proceeded by the word "to"
I am talking to a duck - я говорю утке
--Instrumental Case (Утка - Уткой) = The word in the sentence which is being used, in general think of it being the word in the sentence that could be proceeded by the word "with"
I am drinking coffee with a duck - я пью кофе с уткой
This explains the cases very generally. There are a lot of rules about which prepositions/verbs use which cases and it isn't always 100% consistent with what you would expect in English, for example the verb "to Help" eg. I am helping a duck. You would expect that Duck should use the accusative case, but this verb instead is used with dative case
я помогаю утке - I am helping to a duck
Hope this makes it a bit easier.
It seems genitive but in reality is ACCUSATIVE. For male nouns you need to check whether the noun is animate or inanimate. inanimate = NOMINATIVE animate = GENITIVE
In this case husband муж is animate so the accusative is equal to the GENITIVE мужа and you have to match the adjective to the ACCUSATIVE MASCULINE case that for animate equates to the GENITIVE.
I hope it makes sense.