What Is Their Main Difference?
The main difference between 'with' and 'through' is in what they indicate. 'With' as a preposition is used to indicate companions of an action or event. 'Through' as a preposition is used to indicate the passage from one location to another.
'With' and 'through' as prepositions are used to indicate that an action was done using something. However, there is a distinction. 'With' tends to talk about the instruments that were used while 'through' is more focused on 'by means of' and 'by the agency of.'
I got my phone
She killed her husband
'Through' can be used to indicate movement into one side of something and out of the other side of it.
He had a hard time finding his way
'With' is used to show possession. It can be the possession of a feature or an object. Have a look:
Are They Interchangeable?
They are not interchangeable. Even though both at times represent the meaning 'using' but even in that case, they cannot replace one another as the meaning will be deeply affected.