My filing status is Married Filing Jointly, and our Household income is >$191,000. However, my spouse and my income separately is less than $191,000. My spouse is covered by a retirement plan at work, but I am not. Would I be eligible to contribute to a Roth IRA?
As @DilipSarwate mentioned in his comments, if you are filing Married Filing Jointly and your MAGI for Roth IRA purposes is more than $191K, neither of you can contribute to a Roth IRA. Whether either of you is covered by a retirement plan at work is not relevant.
As @Miro mentioned in the comments, there is a technique called a "backdoor Roth IRA contribution" that is pretty much the same but has no income limit. You contribute to a Traditional IRA, and then immediately convert it to a Roth IRA (neither of these things has an income limit). Note that in order for this work properly, you must not have any pre-tax money in Traditional IRA or other pre-tax IRAs to begin with. If you don't have any existing pre-tax IRA money, then you don't pay any taxes as part of this procedure, and the result of this procedure is pretty much identical in every way to a regular Roth IRA contribution.