To the OP:
Most of the "math" jobs that are currently in the demand fall into one of 3 categories:
a. jobs involving a significant amount of programming or software development
b. statistics or data science type of jobs
c. jobs involving some aspect of economics or finance (including actuarial work -- please note that this category also includes jobs in categories 1 & 2).
It seems to me that your academic background and experience is lacking in any of categories a-c, hence the difficulty in finding employment. Which means that to be competitive you need to do the following:
1. Build up your programming skills -- learn languages like C, C++, Python, etc. You can do this either by taking college courses, online courses like Coursera and edX, or through self-teaching. I would also suggest you post whatever code you develop in open source platforms like Github, so that you can demonstrate your skills.
2. If you are interested in statistics or data science, see if you can take more courses in statistics or machine learning (either through college courses or through places like Coursera and edX, as suggested in advice #1 earlier). You did state that you have a basic understanding of probability, which is good, but you need to build on this. If you are especially considering data science, participate in Kaggle competitions (
www.kaggle.com) and build or incorporate your own machine learning/statistics algorithms to problems identified -- again, having something like this out there will help you out. Become familiar with the basic tools used (like SQL, R, SAS, Pig, Hadoop, Mapreduce, etc.). MarneMath can give you more specific suggestions on data science.
3. Related to #2, since you state you have a BA in biochemistry and a masters in applied math, you would be a prime candidate for biostatistics positions (i.e. the application of statistics in the biomedical field). Consider applying for a second masters in biostatistics.
4. Network, network, network! Attend conferences in your local area, meet and talk to people, set up a LinkedIn profile (if you haven't done so already).