The criminal act of concubinage is present when a husband commits any of the following acts:
(a) Keeping a mistress in the conjugal dwelling;
(b) Having sexual intercourse with a woman other than his wife under scandalous circumstances; or
(c) Cohabiting with a woman not his wife.
Under our criminal law, when a married woman had sexual intercourse with a man not her husband, the married woman commits adultery. The same is not true when a married man had sexual intercourse with a man not her wife. Mere sexual intercourse by a married man to a woman not her wife is not punishable. Unfair for the female species? Probably, but it is the law.
Note that under paragraph (b), in order for concubinage to be present, the sexual intercourse must be under scandalous circumstances. For example: Husband had sex with a woman not his wife inside an elevator of a commercial building.
Under paragraph (a), having a mistress does not per se constitute concubinage. In order to constitute concubinage, the married man must have a mistress and keeps her in the conjugal dwelling. Meaning, the mistress actually lives in the same house where the married couple is residing. For example: Husband having sexual relationship with the housemaid.
Under paragraph (c), there is concubinage if the married man cohabits with a woman not her wife. Meaning, the married man lives together with the other woman under circumstances that will lead others to believe that they are husband and wife. For example: Husband lives together with a woman not his wife and they represent to the community that they are husband and wife.
Your story is not that clear but if it falls in any of the 3 instances, you can file a criminal complaint for concubinage. However, you have to include in your complaint both your husband and his other girl (if she has knowledge that your husband is married). Otherwise, your complaint will not prosper. Also, you must not have pardoned (forgive) your husband and his other girl so that you will not be precluded from filing the criminal complaint.
Please also note that in concubinage, the penalty to be imposed against the concubine (your husband’s girl) is only destierro, meaning, she is only prohibited from residing in a certain place. In other words, the “concubine” will not be imprisoned.
Aside from the criminal case for concubinage, you also have the option to file other cases, such as: (a) civil case for damages; and (b) administrative complaint with the PRC (since you mentioned that she is a teacher). You may want to try to have her license removed for immorality.