The following is the response of the maraji’ to your question:

1. Khamenei: If it doesn’t entail using his wealth/belongings [without his consent], there is no need for permission, but please do remember that it is impermissible to develop a relationship with a non-mahram which usually leads to problems/corruption, or there are chances of it entailing sin.

2. Sistani: Any form of relationship with a non-mahram is impermissible.

3. Saafi Golpaygani: Generally, these forms of relationships are impermissible even if the husband is content with them.

4. Hadavi Tehrani: If the relationship over the internet is a legitimate one and isn't problematic, it is permissible and there is no need for the husband’s permission.

Link to the Istifta’at site