I think this depends on the municipality, but in central Amsterdam, at least, milk cartons go with the plastic:
Drankkartons
Drankkartons kunt u aanbieden bij het plastic verpakkingsmateriaal. In de
fabriek worden de drankkartons eruit gehaald en apart verwerkt.
Drankkartons horen dus niet bij het oud papier. Het is belangrijk dat de
pakken leeg zijn. Verpakkingen van chemisch afval zoals terpentineflessen,
folies zoals chipszakken en piepschuim mogen niet.
Source: https://www.amsterdam.nl/afval/afvalwijzers/afvalwijzer-centrum/ (or actually from the PDF document linked at that page: https://www.amsterdam.nl/publish/pages/692048/afvalwijzer_centrum_2016-2.pdf).
Apparently that document is available in English, but I didn't see it, so I offer my own translation:
Drink cartons
You can recycle drink cartons with plastic packaging. In the recycling facility, the cartons are taken out and processed separately. Drink cartons therefore don't belong with the paper. It is important that the cartons be empty. Packages for chemical waste such as terpentine bottles, foils such as bags of chips, and styrofoam are not allowed.
The paper rules:
Papier en karton
Papier en karton (schoon, droog en zonder plastic omslag) kunt u kwijt in de
papiercontainer. Grote stukken karton maakt u klein zodat het door de
opening past. Lukt dit niet? Zet het dan niet naast de container maar biedt
het aan bij uw huisvuil.
Tip: wilt u minder papier, maar wel op de hoogte blijven van alle
aanbiedingen? Download dan de gratis app Spotta en haal de gratis
nee/nee sticker op bij een van de stadsloketten. Zo blijft u toch op de
hoogte van alle aanbiedingen in uw buurt. Dat scheelt een hoop!
Translated:
Paper and cardboard
You can deposit paper and cardboard (clean, dry, and without plastic covering) in the paper container. Large pieces of cardboard must be broken into smaller pieces to fit through the opening. If you cannot make the cardboard fit in the opening, do not leave it by the container, but put it with your household trash.
Tip: If you want less paper, but still want to know about offers, download the free Spotta app and get the free "nee/nee" sticker from one of the stadsloketten. This way, you'll stay on top of all the offers in your neighborhood. That will save you a lot!
The leaflet doesn't mention this, but in the recycling programs I'm familiar with, magazine-type glossy paper is permitted; it does not contain plastic. My usual test is to tear it -- this usually makes it obvious whether the paper has a plastic coating or some other form of glossy coating.