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