That's not correct.
You always use the lower of your resistances when hit with multi-typed damage.
However, immunity is paramount. If you're immune to cold, you're immune to fire&cold damage, fire&lightning&cold, etc. "A creature that is immune to a damage type (such as cold or fire), a condition (such as dazed or petrified), or another specific effect (such as disease or forced movement) is not affected by it."
However, immunity to a damage type doesn't immunize you from the non-damaging effects of that type -- immuity to charm, fear, illusion, poison, or sleep will protect from non-damaging effects of powers with those types (and poison is both an effect and a damage type, so poison immunity does double duty), but fire or cold immunity won't.
Back to the topic, note that the verbage above is absolute. Combined damage types are hit with both immunities (ooh, if you do 3 fire damage and 25 radiant and necrotic damage, fire immunity will only stop 3 damage, despite the attack getting all three keywords and benefiting from all three vulnerabilities).
Note the difference in the language on resistance: "Against Combined Damage Types: Your resistance is ineffective against combined damage types unless you have resistance to each of the damage types, and then only the weakest of the resistances applies. For example, if you have resist 10 lightning and resist 5 thunder and an attack deals 15 lightning and thunder damage to you, you take 10 damage, because the resistance to the combined damage types is limited by the lesser of the two resistances."