Learn English – “India has” or “India have”

Perfect constructions speak about a state which obtains at Reference Time—the time which your discourse addresses—as a result of some prior event. Present perfect and past perfect address different Reference Times.

Present perfect speaks about a present Reference Time:

I am about to start my first novel, but I have been writing since childhood. ... This speaks about my present writing experience.

Past perfect speaks about a past Reference Time:

In 2003 I started my first novel, but I had been writing since childhood. ... This speaks about my writing experience in 2003.

You may read more (much more, possibly, than you want) about the meaning and use of perfect constructions here.

Damkerng T is right that "family" can be treated as singular or plural:

Collective nouns, or collectives (family, team, couple, etc.), tend to be plural when the component members are considered separately and singular when the group is handled as a unit

So:

1) "My family is great."

or

2) "My family are great."

These mean the same thing - it's just that, in 2), the speaker is emphasising the individual members of their family, rather than the family as a group. It really means "My family (members) are..."

Of course, your example sentence does not say "...that the family is ..."

Instead, it is giving two subjects: parents and family, which suggests that "are" is better here. Possibly the writer is thinking of parents as part of "the family", so groups both items together with the singular "is".

The fact remains, there are two subjects given, even if one is part of the other, so the plural "are" should follow (grammatically speaking).

To emphasise that one is part of the other, "the family (especially/including parents) is..." would be better.