In models with two (or more) Higgs doublets, there are five or more Higgs bosons, rather than one as in the Standard Model. The four extra Higgs bosons are customarily called H+, H-, A and h (or H), with H and h being CP-Even Higgs one heavier and one lighter, and A being a CP-Odd Higgs boson.
The A is excluded with 95% confidence at masses from 220 GeV to 1000 GeV by existing LHC measurements by the ATLAS experiment. Two Higgs doublets are generically present in all SUSY models and in many other non-SUSY models beyond the Standard Model as well.
The 125 GeV Higgs boson is CP-Even as expected.
Meanwhile, the CMS experiment has produced more SUSY exclusions, because there is still not any sign of supersymmetry at the LHC.
Previous discussions of the theoretical and experimental barriers to two Higgs doublet models also dis favor the model, but a two Higgs doublet model has been proposed to explain multiple modest anomalies in LHC data.
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