Which is correct grammatically?
Sein Haus und Garten ist schön.
Sein Haus und Garten sind schön.
I tend to think the former is correct by taking Sein Haus und Garten as a singular subject. Is this right?
There is an old german song that goes...
"Marmor, Stein und Eisen bricht"
even there it´s wrong, because it must be
"Marmor, Stein und Eisen brechen"
in colloquial language you actually hear that a lot. So if you make a mistake when talking to somebody, most german people won´t even notice. But it´s still not right to use the singular here.
Like marstato says, you're talking about more than one object, so the plural applies:
Sein Haus(1) und Garten(2) sind schön.
OTOH if you say
Sein Haus mit Garten ist schön.
then "Haus mit Garten" becomes a single object, and then the singular applies.
Note: a common error in many languages is to use the plural form also for "a number" or "a lot":
There are a number of options.
(Can somebody make this an example in German?) This is wrong. There may be many things (plural), but "a number" is singular. The correct form is
There is a number of options.
You don't say
Da sind eine Dose mit Murmeln.
either, do you?