Since you don't specify an age, I have two answers for you, one for ecclesiastical Latin and one for classical.
In short: familia and (apparently) familiaris consortio are good in church Latin.
Indeed, in ecclesiastical Latin, familia is used commonly (shall I even say perferably?) in this sense. A prominent example is a 1981 document by Pope St. John Paul II, titled Familiaris Consortio on the role of the christian family in the modern world (quote from the official English translation).
It even seems, that the title itself was intended to further exclude ambiguity from the meaning. All the official translations I can understand, straightforwardly translate familiaris consortio in the text as family. (And from the document it is pretty clear it refers to the nuclear family).
Regarding classical Latin, I am pretty convinced that there is no single word to mean family in the modern sense, and that the disambiguation must come from context or from more words. The L&S entry on familia offers a relevant argument and a few alternatives, when enumerating the meanings in the main entry:
the slaves in a household, a household establishment, family servants, domestics (not = family, i. e. wife and children, domus, or mei, tui, sui, etc., but v. II. A. 3 infra [emphasys mine]
So it's generally not equal to family, for which you have domus and the possessives (both obviously ambiguous), or something like parentes filiique (or uxor filiique mei, etc.), as discussed in the comments to your question.
The referred meaning II. A. 3 clearly states:
a family, the members of a household, = domus (rare), [emphasys mine, again]
(which I think is what we all knew: it can mean family, but this meaning is rare and for that the word domus is better, even if its primary meaning is house).