Haven't heard the use of "house" in connection with an apartment. In my opionion it would be mesleading or lead to misunderständings if you used "house" that way.

My daughters' friends in Canada always asked "Can I come to your house?' when they wanted to have a playdate. (No matter whether the family was living in a house or appartment)
House in this context = where you live

Birgila:

That would support the last use of house as a cover term. But would they or your daughter also say it of their own apartments (You can come over to my house)?

I would avoid using "house" to describe an apartment. Some years ago, I misspoke and called my apartment a house (I had grown up in a house and was relatively new to apartment living). My friends were confused and asked if I had moved! "Home" is more generic and can refer to an apartment, especially in the phrase "I am going home." But even in this case, many people would still use the word apartment, e.g., "I am going back to my apartment." (This applies to U.S. usage; I don't know about British usage.)

I grew up in an apartment house (in New York) and we children would always invite playmates to "come to my house". As an adult, I understand the difference between "house" and "apartment", but as children we didn't care about such nuances.

Something else commonly used, for house or apartment is "place". Let's go to my place. Your place is really much closer.

I agree with Peter S that adults would differentiate, but children would probably use house no matter what the architecture. eg., (very) young boy to friend: she has a really cool house - it's an apartment.... :)

In a general sense, your house is just "where you live" as birgila said. So it doesn't matter if it is a flat, apartment, semi-detached house, villa, or mansion - your home is your house. Where German speakers say "Wohnung" we would often simply say "house" in English.
e.g. don't play ball games in the house (it would sound odd to say "in the flat" here)