In Poland We do it exactly as you said:
Street_name street_number/house_number
Postal_code, City, Country
Street_name street_number/house_number
Postal_code, City, Country
10 Downing Street
London
SW1A 2AA
(The postcode is least-specific first: SW is South West London, 1 is the district nearest Central London, and the 2 would usually be a few streets and the AA 5-10 houses, but this is a unique code for an address that gets a lot of post.)Of course that's arguable, as postcode shouldn't really be considered a component of-, rather an alternative to- other sections of the address.