You won't need a new visa untill your multiple entry visa (printed by the Greeks) expires.
When your visa expires in the future you could ask for a new visa, which should be free. Just like your visa to Greece should have been free if you IDed yourself as a family member joining the EU/EAA national. All embassy websites should have info on EU/EAA spouse, sadly not all do ( violating the EU rules).
If the EU webpage is not clear enough, check the freedom of movement act. 2004/38/EC.
See PDFs and check article 1-6:
http://eur-lex.europa.eu/legal-content/ ... 32004L0038
As far as supporting documents for EU/EAA spouse go:
3.6. Supporting documents
In order to prove that the applicant has the right to be issued with an entry visa under the
Directive, he must establish that he is a beneficiary of the Directive. This is done by
presenting documents relevant for the purposes of the three questions referred to above, i.e.
proving that:
• there is an EU citizen from whom the visa applicant can derive any rights;
• the visa applicant is a family member (e.g. a marriage certificate, birth certificate,
proof of dependency, serious health grounds, durability of partnerships …) and his
identity (passport); and
• the visa applicant accompanies or joins an EU citizen (e.g. a proof that the EU
citizen already resides in the host Member State or a confirmation that the EU
citizen will travel to the host Member State).
It is an established principle of EU law in the area of free movement that visa applicants have
the right of choice of the documentary evidence by which they wish to prove that they are
covered by the Directive (i.e. of the family link, dependency …). Member States may,
however, ask for specific documents (e.g. a marriage certificate as the means of proving the
existence of marriage), but should not refuse other means of proof.
For further information in relation to the documentation, see Commission Communication
COM (2009) 313 final 26 .
Source: Schengen Visa Handbook
http://ec.europa.eu/dgs/home-affairs/po ... 620_en.pdf
Basically you will need your marriage document, passports of the applicant, passport of EU citizen, statement from the EU citizen and optionally but if possible a transport ticket reservation such as a ferry reservation from Dover to Calais.
Finally TLS (and VFS) are optional, direct access must be maintained and if the embassy does a proper job they do mention this.